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What Do We Really Know about Cosmic Acceleration?
Abstract
Essentially all of our knowledge of the acceleration history of the Universe - including the acceleration itself - is predicated upon the validity of general relativity. Without recourse to this assumption, we use SNeIa to analyze the expansion history and find (i) very strong (5 sigma) evidence for a period of acceleration, (ii) strong evidence that the acceleration has not been constant, (iii) evidence for an earlier period of deceleration and (iv) only weak evidence that the Universe has not been decelerating since z~0.3.
... In the model-dependent parametric approach, one assumes a priori a specific functional form of kinematic quantities, such as the deceleration function q(z), and a probability distribution of the data [16][17][18][19]. A feature of this strategy is that its results have potentially smaller error bars when compared to the others. ...
... Among these approaches is the Principal Component Analyses (PCA), in which the kinematic function is described in terms of a set of basis JCAP09(2015)045 functions and the data is used to determine which subset of this basis is better constrained. Then, the function is reconstructed by using this subset [13,17,[20][21][22][23]. ...
... For example, in refs. [16][17][18][19] they fit different functional forms of the deceleration function q(z). The drawback of this method is that the choice of a functional form introduces a form-bias in the estimates if the functional form is different from the true one. ...
Distance measurements are currently the most powerful tool to study the expansion history of the universe without specifying its matter content nor any theory of gravitation. Assuming only an isotropic, homogeneous and flat universe, in this work we introduce a model-independent method to reconstruct directly the deceleration function via a piecewise function. Including a penalty factor, we are able to vary continuously the complexity of the deceleration function from a linear case to an arbitrary (n+1)-knots spline interpolation. We carry out a Monte Carlo (MC) analysis to determine the best penalty factor, evaluating the bias-variance trade-off, given the uncertainties of the SDSS-II and SNLS supernova combined sample (JLA), compilations of baryon acoustic oscillation (BAO) and H(z) data. The bias-variance analysis is done for three fiducial models with different features in the deceleration curve. We perform the MC analysis generating mock catalogs and computing their best-fit. For each fiducial model, we test different reconstructions using, in each case, more than 10⁴ catalogs in a total of about 5× 10⁵. This investigation proved to be essential in determining the best reconstruction to study these data. We show that, evaluating a single fiducial model, the conclusions about the bias-variance ratio are misleading. We determine the reconstruction method in which the bias represents at most 10% of the total uncertainty. In all statistical analyses, we fit the coefficients of the deceleration function along with four nuisance parameters of the supernova astrophysical model. For the full sample, we also fit H0 and the sound horizon rs(zd) at the drag redshift. The bias-variance trade-off analysis shows that, apart from the deceleration function, all other estimators are unbiased. Finally, we apply the Ensemble Sampler Markov Chain Monte Carlo (ESMCMC) method to explore the posterior of the deceleration function up to redshift 1.3 (using only JLA) and 2.3 (JLA+BAO+H(z)). We obtain that the standard cosmological model agrees within 3σ level with the reconstructed results in the whole studied redshift intervals. Since our method is calibrated to minimize the bias, the error bars of the reconstructed functions are a good approximation for the total uncertainty.
... It is closely related to the weaker assumption that space-time is homogeneous and isotropic, so that the FRW metric is still valid, as are the kinematic equations for redshift/scale factor. Some call it cosmography [20,22] or cosmokinetics [23], others use the term Friedmannless cosmology [24,25], but, in what follows, we refer to it simply as a kinematic approach since it holds true regardless of the underlying cosmic dynamics [3,26,27,28,29,30]. ...
... where P (p) is the prior probability distribution for the parameters, which we adopt to be flat, and V P is the volume in the parameter space defined by the prior intervals. We chose conservative prior intervals (see table 1) based on physical considerations and "prior" information, i.e. previous results obtained with older and smaller SNIa samples [22,25,27,34]. The prior boundaries are chosen to be large enough so most of the likelihood is retained in the integration (19), but not too large to do not excessively penalize the Bayesian evidence through V P. For all the models considered here, except for M 2 , as will be discussed in the next section, the 3σ boundaries in the likelihood are well inside the prior volume, so the Bayesian evidence decreases linearly with V P. We are able to compare models by calculating the Bayes factor between any two models M i and M j , which we define as ...
... The panel for M 2 shows a qualitatively similar plot to the last panel of figure 2 of Shapiro & Turner [22]. The z t marginalized likelihood contours for M 2 at 2σ and 3σ confidence levels show that the data do not constrain strongly the deceleration parameter for redshifts above the transition. ...
The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter (constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter (constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today ( and ) and for the transition redshift () between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the confidence limits imply the following ranges of values: , and , which are compatible with the CDM predictions, , and . We find that even very simple kinematic models are equally good to describe the data compared to the concordance CDM model, and that the current observations are not powerful enough to discriminate among all of them. Comment: 13 pages. Matches published version
... A more robust form is a non-parametric reconstruction which attempts to build up the actual functional form of f w.r.t. z directly from the observational data [92,[215][216][217][218][219][220][221][222][223][224][225][226][227][228]. ...
... There are several methods for implementing a non-parametric reconstruction in cosmology. These include the Principal Component Analysis (PCA) [217][218][219], Local Regression Smoothing (LRS) [220,221], Genetic Algorithms (GA) [222][223][224] and Gaussian Process (GP) [225][226][227][228]. This thesis is devoted to studying the non-parametric reconstruction of some cosmological parameters by adopting the GP formalism. ...
The present thesis is devoted to the non-parametric reconstruction of some cosmological parameters using diverse observational datasets. The Universe is assumed to be spatially homogeneous and isotropic, thus described by the FLRW metric. The first chapter provides a brief introduction to cosmology and focuses on the reconstruction methods. An assessment of the cosmic distance-duality relation is discussed in chapter 2. In chapter 3, a non-parametric reconstruction of the cosmological jerk parameter is carried out. Chapter 4 explores the possibility of a non-gravitational interaction in the cosmic dark sector. In chapter 5, attempts are made to revisit a non-parametric reconstruction of the cosmic deceleration parameter using various combinations of recently updated background datasets and the growth rate of structure measurements from the redshift-space distortions. Finally, chapter 6 contains the concluding remarks and relevant discussion regarding the overall work presented in the thesis.
... The parameter corresponding to such a transition from decelerated to an accelerated phase is referred to as the transition redshift and it may be treated as a new cosmic parameter along with the present deceleration parameter 0 and the Hubble constant 0 . It is now commonly accepted that the upper bound on the transition redshift is less than unity, which has been confirmed by multiple independent investigations in both model-dependent and model-independent approaches (Farooq et al. (2013b) ;Farooq & Ratra (2013); Sharov & Vorontsova (2014); Shapiro & Turner (2006); Cunha & Lima (2008); Rani et al. (2015); Lima et al. (2012); Moresco et al. (2016); Jesus et al. (2018); Velasquez-Toribio & Magnago (2020)). Shapiro & Turner (2006) in their analysis adopted a model-dependent approach and using SN Type Ia observations, they put a constraint on the deceleration parameter ( ) and transition redshift . ...
... It is now commonly accepted that the upper bound on the transition redshift is less than unity, which has been confirmed by multiple independent investigations in both model-dependent and model-independent approaches (Farooq et al. (2013b) ;Farooq & Ratra (2013); Sharov & Vorontsova (2014); Shapiro & Turner (2006); Cunha & Lima (2008); Rani et al. (2015); Lima et al. (2012); Moresco et al. (2016); Jesus et al. (2018); Velasquez-Toribio & Magnago (2020)). Shapiro & Turner (2006) in their analysis adopted a model-dependent approach and using SN Type Ia observations, they put a constraint on the deceleration parameter ( ) and transition redshift . By considering different dynamical dark energy models, Melchiorri et al. (2007) put constraints on . ...
One of the most significant discoveries in modern cosmology is that the universe is currently in a phase of accelerated expansion after a switch from a decelerated expansion. The precise determination of the time of this transition from a decelerated phase to an accelerated phase has been a topic of wide interest. This redshift is commonly referred to as the transition redshift . This paper aims to put constraints on the transition redshift with both model-dependent and model-independent approaches. We divide this paper into two parts. In first part we follow a model dependent approach. Here, we consider a non-flat CDM model as a background cosmological model and use the Hubble parameter measurements of 33 datapoints to construct the cosmic triangle. Further we reconstruct another cosmic triangle plot between , and where the constraints of each parameter are determined by the location in this triangle plot. Using and values, we find the best value of transition redshift , which is in good agreement with the Planck 2018 results at confidence level. The second part is based on a non-parametric method. We plot a Hubble Phase Space Portrait (HPSP) between and H(z). From this HPSP diagram, we estimate the transition redshift as well as the current value of equation of state parameter in a model-independent way. We find the best fit value of and . We also simulate the observed Hubble parameter measurements in the redshift range and perform the same analysis to estimate the transition redshift.
... The latter part of the 20 th century witnessed a dramatic change in cosmology with the emergence of compelling observational evidence supporting the accelerated expansion of the universe. This phenomenon, which appears to have commenced relatively recently in cosmic history, has been corroborated by multiple independent lines of evidence [1]. Notably, observations of Type Ia supernovae [2,3,4], analyses of large-scale cosmic structure [5,6], measurements of Cosmic Microwave Background Radiation (CMBR) anisotropies [7,8], and studies of Baryon Acoustic Oscillations [9,10] have all contributed to this paradigm-altering discovery. ...
We present a comprehensive investigation exploring the theoretical framework of Einstein-Aether gravity theory when combined with two novel cosmological paradigms: the Barrow Agegraphic Dark Energy (BADE) and its newer variant, the New Barrow Agegraphic Dark Energy (NBADE). Our study focuses on deriving the functional relationships within Einstein-Aether gravity as they emerge from these dark energy formulations. The parameter space of our theoretical models is rigorously constrained through statistical analysis employing the Markov Chain Monte Carlo (MCMC) methodology, utilizing multiple observational datasets, incorporating measurements from cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the combined Pantheon+SH0ES compilation. Based on our optimized parameter sets, we conduct an extensive analysis of fundamental cosmological indicators, including cosmographic parameter evolution, dark energy equation of state parameter (), evolution of the density parameter , dynamical characteristics in the space, behavior of statefinder diagnostic pairs and (r,q), and Om(z) diagnostic trajectories. Our analysis demonstrates that the current cosmic expansion exhibits accelerated behavior, with the dark energy component manifesting quintessence-like properties in the present epoch while trending toward phantom behavior in future evolution. We additionally evaluate the viability of both BADE and NBADE frameworks through an examination of the squared sound speed () stability criterion. The cumulative evidence suggests that these models effectively characterize contemporary cosmic evolution while offering novel perspectives on dark energy phenomenology.
... This seems to be the case when SNe Ia data are used to constrain flat ΛCDM model parameters; for instance, Rubin et al. (2023) We also use Bayesian evidence (Kass & Raftery 1995;Trotta 2008) It is also necessary to test whether the overall findings are model independent. Hence, we repeat the above analysis by replacing the flat ΛCDM model with the cosmography model (Turner & Riess 2002;Visser 2004;Shapiro & Turner 2006;Xu & Wang 2011). In the spatially flat scenario, the cosmography model parameter set is p = (H 0 , q 0 , j 0 , s 0 ), where q 0 , j 0 , and s 0 denote the present-day values of the deceleration, jerk, and snap parameters, respectively. ...
We systematically explore the influence of the prior of the peak absolute magnitude ( M ) of Type Ia supernovae (SNe Ia) on the measurement of the Hubble constant ( H 0 ) from SNe Ia observations. We consider five different data-motivated M priors, representing varying levels of dispersion, and assume the spatially flat ΛCDM cosmological model. Different M priors lead to relative changes in the mean values of H 0 from 2% to 7%. Loose priors on M yield H 0 estimates consistent with both the Planck 2018 result and the SH0ES result at the 68% confidence level. We also examine the potential impact of peculiar velocity subtraction on the value of H 0 and show that it is insignificant for the SNe Ia observations with redshift z > 0.01 used in our analyses. We also repeat the analysis in the cosmography model and find very similar results. This suggests that our results are robust and model independent.
... Another way to study the cosmic evolution is through the socalled cosmographic or kinematic models (Visser 2004 ;Blandford et al. 2005 ;Visser 2005 ;Elgaroy & Multamaki 2006 ;Shapiro & Turner 2006 ;Rapetti et al. 2007 ;Riess et al. 2007 ), where one is not worried about the Universe composition, but instead, how it evolves. In such models, we seek for direct measures of expansion through its kinematic parameters (such as the Hubble parameter H 0 , E-mail: s.pereira@unesp.br ...
By using recent H(z) and SNe Ia data, we reconstruct the evolution of kinematic parameters H(z), q(z), jerk and snap, using a model-independent, non-parametric method, namely, the Gaussian Processes. Throughout the present analysis, we have allowed for a spatial curvature prior, based on Planck 18 constraints. In the case of SNe Ia, we modify a python package (GaPP) in order to obtain the reconstruction of the fourth derivative of a function, thereby allowing us to obtain the snap from comoving distances. Furthermore, using a method of importance sampling, we combine H(z) and SNe Ia reconstructions in order to find joint constraints for the kinematic parameters. We find for the current values of the parameters: H0 = 67.2 ± 6.2 km/s/Mpc, , , at 1σ c.l. We find that these reconstructions are compatible with the predictions from flat ΛCDM model, at least for 2σ confidence intervals.
... (2.2), (2.3), (2.4), (2.5), (2.6) (see also eqs. (2.13), (2.14), (2.15), (2.16), (2.17) in terms of the comoving distance and its derivatives) in the section 2. In the last few years, this kinematics approach has been studied extensively although in different names, for examples cosmography [9][10][11][12][13][14][15], cosmokinetics [16,17], or Friedmannless cosmology [18,19]. For recent progress, please see refs. ...
In this paper, we firstly calibrate the Amati relation (the E p - E iso correlation) of gamma ray bursts (GRBs) at low redshifts ( z < 0.8) via Gaussian process by using the type Ia supernovae samples from Pantheon+ under the philosophy that objects at the same redshift should have the same luminosity distance in any cosmology. As a result, this calibration derives the distance moduli of GRBs at high redshifts ( z > 0.8). For an application of these derived distance modulus of GRBs to cosmology, via Gaussian process again, a series of cosmography parameters, which describe kinematics of our Universe, up to the fifth order and the redshift z ∼ 5, i.e. the Hubble parameter H ( z ), the deceleration parameter q ( z ), the jerk parameter j ( z ), the snap parameter s ( z ) and the lerk parameter l ( z ), are reconstructed from the cosmic observations. The reconstructed cosmography parameters show a transition singularity at z ∼ 6, it may resort to two possible explanations: one is that the GRBs data points at high redshift z > 5 are still reliable, it means that new physics beyond the ΛCDM model happens; another one is that the quality and quantity of GRBs data points at high redshift z > 5 are not good enough to give any viable prediction of the kinematics of our Universe. To pin down this problem, more high redshifts z > 5 cosmic observational are still needed.
... In the study of the generalized holographic dark energy model, some well-known parametrization type models have been considered [22,23]. Till now, some authors have assumed some possible forms of parametrization of deceleration parameter [24][25][26][27][28][29][30][31][32][33][34][35]. The main advantage behind introducing a parameterization of the deceleration parameter is to provide a framework that is independent of specific gravitational theories. ...
Confirmation of accelerated expansion of the universe probed the concept of dark energy theory, and since then, numerous models have been introduced to explain its origin and nature. The present work is based on reconstructing dark energy by parametrization of the deceleration parameter in the FRW universe filled with radiation, dark matter and dark energy. We have chosen some well-motivated parametrized models 1-3 in an attempt to investigate the energy density in terms of deceleration parameters by estimating the cosmological parameters with the help of different observational datasets. Also, we have introduced a new model 4 for the parametrization of the deceleration parameter. Then we analyzed the cosmography parameters using the best-fit values of the parameters. Using the information criteria, we have examined the viability of the models.
... In the study of the generalized holographic dark energy model, some well-known parametrization type models have been considered [18,19]. Till now, some authors have assumed some possible forms of parametrization of deceleration parameter [20][21][22][23][24][25]. The main advantage of the parameterization deceleration parameter is that the final outcome may not depend on any particular gravitational theory. ...
Confirmation of accelerated expansion of the universe probed the concept of dark energy theory, and since then, numerous models have been introduced to explain its origin and nature. The present work is based on reconstructing dark energy by parametrization of the deceleration parameter in the FRW universe filled with radiation, dark matter, and dark energy. We have chosen some well-motivated parametrized models 1-3 in an attempt to investigate the energy density in terms of deceleration parameters by estimating the cosmological parameters with the help of different observational datasets. Also, we have introduced a new model 4 for the parametrization of the deceleration parameter. Then we analyzed the cosmography parameters using the best-fit values of the parameters. Using the information criteria, we have examined the viability of the models.
... Hence from the physical point of view, the treatment of consideration of the deceleration parameter is better than the consideration of the Hubble parameter. Till now, some authors have considered [6][7][8][9][10][11] the possible parametrizations of deceleration parameter [12][13][14][15][16][17][18][19]. Capozziello et al. [20] assumed on q-parametrization also. ...
In this work, we have assumed the non-flat FRW model of the universe. We probed the optical depth behavior of a few cosmological models, including the deceleration parameter’s parametrized form. We have considered ten such models and carried out a qualitative analysis graphically. We found that these particular lensing phenomena depend greatly on the various parametrization forms of deceleration parameter in the cosmological models. Then we compared these models to each other as well as with [Formula: see text]CDM model.
... 0 z consistent with the observational data, for more details, see Refs. [21][22][23][24][25][26][27][28]. One cannot find a numerical value or observations of the redshift before and during the Big Bang. ...
In this article, we assume that the beginning of the universe was before the Big Bang. In the beginning, all matter in the universe was combined in an infinitesimal spherical shape. This sphere was compressed to an incomprehensible value for a period, and then exploded and expanded time and space. We are referring to the negative time before the Big Bang. The evolution of the universe before the Big Bang, passing through the moment of the explosion to the end of the universe at the Big Rip, has been studied. In this article, we try to answer the questions; did the universe exist before the Big Bang? What is the origin of the universe and how did it arise? What are the stages of the evolution of the universe until the moment of the Big Rip? What is the length of time for the stages of this development?
... On the other hand, some works attempt to investigate the history of the Universe independently of dynamical models. These approaches are called cosmography models or cosmokinetic models (Visser 2004(Visser , 2005Blandford et al. 2005;Elgarøy & Multamäki 2006a;Shapiro & Turner 2006;Rapetti et al. 2007). The work of Capozziello, D'Agostino & Luongo (2020) suggests comparing two different parametrizations: auxiliary variables versus Padé polynomials for high redshifts. ...
An approach to estimate the spatial curvature Ωk from data independently of dynamical models is suggested, through kinematic parametrizations of the comoving distance [DC(z)] with third-degree polynomial, of the Hubble parameter [H(z)] with a second-degree polynomial and of the deceleration parameter [q(z)] with first-order polynomial. All these parametrizations were done as function of redshift z. We used SNe Ia data set from Pantheon compilation with 1048 distance moduli estimated in the range 0.01 < z < 2.3 with systematic and statistical errors and a compilation of 31 H(z) data estimated from cosmic chronometers. The spatial curvature found for DC(z) parametrization was . The parametrization for deceleration parameter q(z) resulted in . The H(z) parametrization has shown incompatibilities between H(z) and SNe Ia data constraints, so these analyses were not combined. The DC(z) and q(z) parametrizations are compatible with the spatially flat universe as predicted by many inflation models and data from cosmic microwave background. This type of analysis is very appealing as it avoids any bias because it does not depend on assumptions about the matter content of the Universe for estimating Ωk.
... Determining the exact moment in the history of evolution of the universe in which accelerated phase began is an interesting question, since different models should provide the same result. The parameter that determines such transition from deceleration to an accelerated phase is called transition redshift, z t , which can be treated as a new cosmic parameter [18,19,[21][22][23][24][25][26][27]. A model without a reasonable transition redshift, z t ∼ 0.5 − 1, for instance, fails on explaining current cosmological observations. ...
This paper aims to put constraints on the transition redshift zt, which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to do that, we use the non-parametric Gaussian Process method with H(z) and SNe Ia data. The deceleration parameter reconstruction from H(z) data yields zt=0.59+0.12−0.11. The reconstruction from SNe Ia data assumes spatial flatness and yields zt=0.683+0.11−0.082. These results were found with a Gaussian kernel and we show that they are consistent with two other kernel choices.
... Other authors have also applied alternative techniques to reconstruct the expansion history of the Universe in a model-independent way and derive constraints on the deceleration parameter, e.g. using the smoothing method of refs. [58][59][60], principal component analyses [23,29], Gaussian processes [61], or piecewise natural cubic splines [62]. These methods are interesting and useful, but also have their own drawbacks. ...
We reconstruct in this paper the deceleration and jerk parameters as functions of the cosmological redshift from data on cosmic chronometers (CCH), baryon acoustic oscillations (BAOs), and the Pantheon+MCT compilation of supernovae of Type Ia (SnIa). The reconstruction is carried out with the Weighted Function Regression method, previously introduced by G'omez-Valent & Amendola (2018). It improves the usual cosmographic approach by automatically implementing Occam's razor criterion. This makes our procedure to be more free of model and parametrization dependencies than many other analyses in the literature. The reconstructed functions are fully compatible with the predictions for the concordance model. In addition, we also discuss the confidence level at which we can claim that the Universe (assumed to be flat, homogeneous and isotropic) is currently accelerating. According to Jeffreys' scale and jargon, we find moderate evidence in favor of such speed-up using the data on SnIa+CCH, and very strong one when we also use data on BAOs. The measured current value of the deceleration parameter in the latter case reads q0∼ −0.60± 0.10, and for the deceleration-acceleration transition redshift we find zt∼ 0.80± 0.10. The former is ∼ 6σ away from 0. This is in stark contrast, for instance, with the ∼ 17σ that are found in the context of the flat ΛCDM even without including the BAOs data. This indicates that cosmography and Occam's razor criterion play a crucial role in this discussion, and that estimating the evidence for positive acceleration only in the framework of a particular cosmological model or parametrization is clearly insufficient.
... However, some works have tried to explore the history of the universe without to appeal to any specific cosmological model. Such approaches are sometimes called cosmography or cosmokinetic models [41][42][43][44][45][46], and we will refer to them simply as kinematic models. This nomenclature comes from the fact that the complete study of the expansion of the Universe (or its kinematics) is described just by the Hubble expansion rate H =ȧ/a, the deceleration parameter q = −aä/ȧ 2 and the jerk parameter j = − ... a a 3 /(aȧ 3 ), where a is the scale factor in the Friedmann-Roberson-Walker (FRW) metric. ...
This paper aims to put constraints on the transition redshift , which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to do that, we consider a flat universe and suppose a parametrization for the comoving distance up to third degree on z, a second degree parametrization for the Hubble parameter H(z) and a linear parametrization for the deceleration parameter q(z). For each case, we show that the type supernovae Ia and H(z) data complement each other on the parameter spaces and tighter constrains for the transition redshift are obtained. By combing the supernovae type Ia observations and Hubble parameter measurements it is possible to constrain the values of as , and at 1 c.l., for each framework, respectively. Such approaches provide reasonably model-independent estimates of this cosmological parameter.
... These data point unambiguously to an acceleration in expansion over the last five billion years, a phenomenon that was dubbed dark energy (Turner 2001(Turner , 2002. The cause of this acceleration will be discussed in section 11; for the present we note that the data constitute strong evidence of an acceleration in the rate of cosmic expansion over the last billion years, independent of theoretical models (Shapiro and Turner 2006). In the context of relativistic cosmology, we recall from section 8 that a measurement of q0 is a measure of − ; the data from each team suggested a figure of about -0.4 for this quantity. ...
We present a centennial review of the history of the term known as the cosmological constant. First introduced to the general theory of relativity by Einstein in 1917 in order to describe a universe that was assumed to be static, the term fell from favour in the wake of the discovery of cosmic the expanding universe, only to make a dramatic return in recent times. We consider historical and philosophical aspects of the cosmological constant over four main epochs: (i) the use of the term in static cosmologies (both Newtonian and relativistic; (ii) the marginalization of the term following the discovery of cosmic expansion; (iii) the use of the term to address specific cosmic puzzles such as the timespan of expansion, the formation of galaxies and the redshifts of the quasars; (iv) the re-emergence of the term in today's Lamda-CDM cosmology. We find that the cosmological constant was never truly banished from theoretical models of the universe, but was sidelined by astronomers for reasons of convenience. We also find that the return of the term to the forefront of modern cosmology did not occur as an abrupt paradigm shift due to one particular set of observations, but as the result of a number of empirical advances such as the measurement of present cosmic expansion using the Hubble Space Telescope, the measurement of past expansion using type SN 1a supernovae as standard candles, and the measurement of perturbations in the cosmic microwave background by balloon and satellite. We give a brief overview of contemporary interpretations of the physics underlying the cosmic constant and conclude with a synopsis of the famous cosmological constant problem.
... The value q ≈ −0.5 is the ΛCDM model result. The value depends on the chosen parametrisation[78,79]. The value has also been derived under the assumption that light propagation is related to the expansion rate via the FRW distance-redshift relation, which is not necessarily the case if backreaction is large[17,[22][23][24][25][26]. ...
We evaluate the effect of structure formation on the average expansion rate with a statistical treatment where density peaks and troughs are modelled as homogeneous ellipsoids. This extends earlier work that used spherical regions. We find that the shear and the presence of filamentary and planar structures have only a small impact on the results. The expansion rate times the age of the universe Ht increases from 2/3 to 0.83 at late times, in order of magnitude agreement with observations, although the change is slower and takes longer than in the real universe. We discuss shortcomings that have to be addressed for this and similar statistical models in the literature to develop into realistic quantitative treatment of backreaction.
... If backreaction explains the accelerated expansion, the acceleration is transient and the expansion will at some point start to decelerate [81,82]. The distance data are consistent with (but, obviously, do not require) considerably less acceleration (or even deceleration) today than in the ΛCDM model, as the distance depends on the acceleration via two integrals, and conclusions about q 0 depend on the chosen parametrisation [146,147,[154][155][156][157][158][159][160][161][162][163][164][165][166][167][168][169][170][171][172]. For the BC03+BAO expansion rate data, deceleration today is within the 68% limits for the splines, and well within the 95% contours for the polynomials. ...
If the FRW metric is a good approximation on large scales, then the distance and the expansion rate, as well different notions of distance, satisfy certain consistency conditions. We fit the JLA SNIa distance data to determine the expected amplitude of the violation of these conditions if accelerated expansion is due to backreaction. Adding cosmic clock and BAO expansion rate data, we also model-independently determine the current observational limits on such violation. We find that the predicted maximum backreaction amplitude (95% C.I.) is of the same order as the current observational constraints , the precise numbers depending on the adopted fitting method (polynomials or splines) and stellar population evolution model. We also find that constraints on the value of determined from expansion rate data are sensitive to the stellar evolution model. We forecast constraints from projected LSST+Euclid-like SNIa plus Euclid galaxy differential age data. We find improvement by factor of 6 for the backreaction case and 3 for the model-independent case, probing an interesting region of possible signatures.
... without referring to the dynamics [100,101]. Studies along this line indeed show that q < 0, i.e.,ä > 0, at low redshift [102][103][104]. Sinceä involves the second derivative with respect to time, measurements of the cosmic time or age of the universe at a series of redshifts would give the most direct evidence. ...
The Large Synoptic Survey Telescope (LSST) is a high étendue imaging facility that is being constructed atop Cerro Pachón in northern Chile. It is scheduled to begin science operations in 2022. With an ( effective) aperture, a novel three-mirror design achieving a seeing-limited field of view, and a 3.2 gigapixel camera, the LSST has the deep-wide-fast imaging capability necessary to carry out an survey in six passbands (ugrizy) to a coadded depth of over 10 years using of its observational time. The remaining of the time will be devoted to considerably deeper and faster time-domain observations and smaller surveys. In total, each patch of the sky in the main survey will receive 800 visits allocated across the six passbands with exposure visits.
The huge volume of high-quality LSST data will provide a wide range of science opportunities and, in particular, open a new era of precision cosmology with unprecedented statistical power and tight control of systematic errors. In this review, we give a brief account of the LSST cosmology program with an emphasis on dark energy investigations. The LSST will address dark energy physics and cosmology in general by exploiting diverse precision probes including large-scale structure, weak lensing, type Ia supernovae, galaxy clusters, and strong lensing. Combined with the cosmic microwave background data, these probes form interlocking tests on the cosmological model and the nature of dark energy in the presence of various systematics.
The LSST data products will be made available to the US and Chilean scientific communities and to international partners with no proprietary period. Close collaborations with contemporaneous imaging and spectroscopy surveys observing at a variety of wavelengths, resolutions, depths, and timescales will be a vital part of the LSST science program, which will not only enhance specific studies but, more importantly, also allow a more complete understanding of the Universe through different windows.
... based on a linear parametrization of q(z). Therefore, the inferences of the transition redshift are highly model dependent [38]. What this means is that, observationally, since the optimization of our probe is loosely based on the transition redshift, we recommend that a redshift distribution as broad as possible be used. ...
We present a novel approach to constrain accelerating cosmologies with galaxy cluster phase spaces. With the Fisher matrix formalism we forecast constraints on the cosmological parameters that describe the cosmological expansion history. We find that our probe has the potential of providing constraints comparable to, or even stronger than, those from other cosmological probes. More specifically, with 1000 (100) clusters uniformly distributed in redshift between , after applying a conservative mass scatter prior on each cluster and marginalizing over all other parameters, we forecast constraints on the dark energy equation of state w and matter density parameter of and in a flat universe. Assuming the same galaxy cluster parameter priors and adding a prior on the Hubble constant we can achieve tight constraints on the CPL parametrization of the dark energy equation of state parameters and with just 100 clusters: and . Dropping the assumption of flatness and assuming we also attain competitive constraints on the matter and dark energy density parameters: and for 100 clusters uniformly distributed between . We also discuss various observational strategies for tightening constraints in both the near and far future.
... Pioneering work in the kinematic modelling of cosmic acceleration was by Riess et al. [18] where a linear parametrization of the deceleration parameter has been adopted to estimate the redshift at which the transition from decelerated to accelerated expansion phase occurred. Different parametrization of deceleration parameter have been discussed by Shapiro and Turner [19], Gong and Wang [20], Xu and Liu [21] and Elgaroy and Multamaki [22]. Recently kinematic method to investigate the cosmic acceleration has been discussed by Barboza and Carvalho [23]. ...
The present work deals with a kinematic approach to the modelling the late time dynamics of the universe. This approach is based upon the assumption of constant value of cosmological jerk parameter, which is the dimensionless representation of the 3rd order time derivative of the scale factor. For the CDM model, the value of jerk parameter is -1 throughout the evolution history. Now any model dependent estimation of the value of the jerk parameter would indicate the deviation of the model from the cosmological constant. In the present work, it has also been shown that for a constant jerk parameter model, any deviation of its value from -1 would not allow the dark matter to have an independent conservation, thus indicating towards an interaction between dark matter and dark energy. Statistical analysis with different observational data sets (namely the observational Hubble parameter data (OHD), the type Ia supernova data (SNe), and the baryon acoustic oscillation data (BAO)) along with the cosmic microwave background (CMB) data (namely the CMB shift parameter) lead to a well constrained values of the jerk parameter and the model remains at a very close proximity of the CDM.
... Earlier Shapiro and Turner (2005) used both parametric and non-parametric methods to constrain the deceleration parameter, q(z) and transition redshift, z t using SNe Ia data [15]. Melchiorri et al. (2007) also considered different dynamical dark energy models to put constraints on z t [16]. ...
In this paper, we use the Cosmokinematics approach to study the accelerated
expansion of the Universe. This is a model independent approach and depends
only on the assumption that the Universe is homogeneous and isotropic and is
described by the FRW metric. We parametrize the deceleration parameter, q(z),
to constrain the transition redshift () at which the expansion of the
Universe goes from a decelerating to an accelerating phase. We use three
different parametrizations of q(z) namely,
q_\I(z)=q_{\textnormal{\tiny\textsc{1}}}+q_{\textnormal{\tiny\textsc{2}}}z,
q_\II (z) = q_\3 + q_\4 \ln (1 + z) and
q_\III(z)=\frac{1}{2}+\frac{q_{\textnormal{\tiny\textsc{5}}}}{(1+z)^2}. A
joint analysis of the age of galaxies, strong lensing and supernovae Ia data
indicates that the transition redshift is less than unity i.e. . We also
use a nonparametric approach (LOESS+SIMEX) to constrain . This too gives
which is consistent with the value obtained by the parametric approach.
... Contrary to the dark matter assumption (which is necessary from the scale of galaxies), it is at the scale of the Universe that this dark energy assumption becomes necessary. The main evidence that makes it necessary is the observation of an acceleration of the expansion of the Universe (RIESS et al., 1998;PERLMUTTER et al., 1998) in the last half of its life (SHAPIRO et al., 2005). The gravitational theories (Newtonian and general relativity) can't explain this behavior without dark energy. ...
In a previous paper, we demonstrated that the linearized general relativity could explain dark matter (the rotation speed of galaxies, the rotation speed of dwarf satellite galaxies, the movement in a plane of dwarf satellite galaxies, the decreasing quantity of dark matter with the distance to the center of galaxies' cluster, the expected quantity of dark matter inside galaxies and the expected experimental values of parameters of dark matter measured in CMB). It leads, compared with Newtonian gravitation, to add a new component to gravitation without changing the gravity field (also known as gravitomagnetism). In this article we are going to see that general relativity could also explain dark energy and makes a prediction on gravitational mass of antimatter. To be consistent, this solution implies that gravitational mass of antimatter must be negative and that neutrino is not a Majorana particle. These predictions will be soon tested (AEgIS and NEMO experiments). It gives an explanation of cosmological constant and is consistent with the experimental values of parameters giving the expected order of magnitude for this cosmological constant. It predicts that dark energy (or cosmological constant) is not constant in time. Furthermore, this solution implies a cosmic inflation, leads to an explanation of the apparent disappearance of antimatter and can explain the recent acceleration of the expansion of our Universe. One also predicts several very fundamental testable results on null mass and on antimatter. The photons emitted by anti-Hydrogen should be deviated symmetrically compared to the ones emitted by Hydrogen in a gravitational field. The Lymann spectral lines of anti-Hydrogen should be shifted " symmetrically " compared to the ones of Hydrogen between two altitudes. The principle of equivalence of masses should be violated for antiprotonic helium. More prosaically, it offers an amazing image of our universe at an incredible scale.
... Another published analysis is to determine the parameters of the scale factor a that has been expanded to fifth order polynomial [Joh04]. Instead of considering a special parameterization, a more general approach has been presented in [ST06], where the deceleration parameter q is expanded into principal components. In [RAAB07] the jerk parameter j = 1 ...
... In order to reconstruct the interaction using current data sets, we should find a model-independent method to reconstruct D(z) and its derivatives. While there are several methods such as principle component analysis [19][20][21], Gaussian smoothing [22,23] and Gaussian processes [24][25][26][27], in this paper we will reconstruct D(z) and its derivatives more precisely by using the GP method. ...
We present a non-parametric approach to reconstruct the interaction between
dark energy and dark matter directly from SNIa Union 2.1 data using Gaussian
Processes, which is a fully Bayesian approach for smoothing data. In this
method, once the equation of state (w) of dark energy is specified, the
interaction can be reconstructed with respect to redshift. For the decaying
vacuum energy case with , the reconstructed interaction is consistent
with the CDM model, namely, there is no evidence for the interaction.
This also holds for the constant w cases from to and for the
CPL parameterization case. If the equation of state deviates obviously from
, the reconstructed interaction exits at confidence level. This
shows the degeneracy between the interaction and the equation of state of dark
energy when they get constraints from the observational data.
The statefinder diagnostic is useful to discriminate dark energy models. In this paper, under the minimum assumption of a spatially flat Friedmann–Lemaître–Robertson–Walker Universe, we reconstruct the statefinder pair { r ( z ) , s ( z ) } in addition to the deceleration parameter q ( z ) via the Gaussian process from the cosmic observational data points which include the recently released Pantheon+ SN Ia samples and the observational Hubble data H ( z ). The reconstructed evolution trajectories are shown on the r - q , r - s planes. The reconstructed q ( z ) is consistent with previous studies. Meanwhile, a novel quantity named suitability is introduced on the r - q , r - s planes to assess the validation of a dark energy model.
In this paper, we employ parametrization techniques within the framework of f (T) gravity to investigate the deceleration parameter (DP), a key quantity characterizing the universe's expansion dynamics. By analyzing the DP, we gain valuable insights into the nature of cosmic constituents and their impact on the universe's evolution. We utilize a combination of observational data, including 31 Cosmic Chronometers (CC) measurements, 1048 Type Ia Supernovae (SNIa), 17 Baryon Acoustic Oscillation (BAO) measurements, Cosmic Microwave Background (CMB), 162 Gamma Ray Bursts (GRB), and 24 observations of compact radio quasars (Q). We employ the Markov chain Monte Carlo (MCMC) sampling technique to estimate the best-fit range of model parameters. Cosmological and cosmographic parameters are investigated, and their implications in the context of cosmology have been discussed. We also analyze the statefinder and Om diagnostic to gain deeper insights into the universe's behavior. Furthermore, we conduct statistical analyses to compare our model with the standard ΛCDM model. Our investigation also includes the study of physical parameters, providing comprehensive insights into the cosmological behavior within the f (T) gravity framework. The results and comparisons presented in this work contribute to a deeper understanding of the universe's dynamics and provide valuable implications for the cosmological model under consideration.
In this paper, the emergent universe model (EU) is explored (as per Mukherjee ) in a flat scenario with equation of state (EoS) (where A and B are constants). Here, the temperature function is evaluated in terms of the EoS parameters and redshift under the conditions of balanced particle creation and annihilation. To examine the thermodynamic evolution and find a viable EU model, constraints on its EoS parameters are determined. First, constraints on , and B (where and is the present energy density) are obtained from the acceptable transition redshift limit and decoupling temperature limit as ≈ and B ≈ for the general EU model. Finally, stricter constraints on are drawn from recent and observed Hubble data (OHD). These and values are then utilized to obtain acceptable limits on , and B. On average, the acceptable limits on , , and B are (in the 1 error limit), ≈ and ≈ , respectively, for the general EU model. In the model, obtained value (at the 1 level). The present values of the EoS parameters are determined, and the viability of the models is examined with plots of the deceleration parameter (q), equation of state () and squared adiabatic sound speed () with redshift (z). The distance modulus () of this EU model is compared with the HIIG and Union2.1 data. The models with B , are not suitable at all according to the present analysis, whereas, the model is quite similar to the observations.
In the current paper, a dark energy (DE) model reconstructed from the well‐motivated deceleration parameter (DP) is analyzed. A flat FRW Universe filled with radiation, dark matter (DM), and dark energy fluids is considered. The free parameters are constrained using measurements from Supernovae, Hubble, Gamma Ray Bursts, Quasars, and Baryon acoustic Oscillations. The model under study is found to be very supported by observation with respect to ΛCDM since . Besides, a cosmographic analysis is performed showing that the reconstructed model behaves similarly as ΛCDM does. Finally, a diagnostic analysis is performed reporting that the studied model behaves quintessence type at a late time.
In this paper, we revisit the kinematical state of our Universe via the cosmographic approach by using Gaussian process, where the minimum assumption is the cosmological principle, i.e. the Friedmann–Lemaître–Robertson–Walker metric. A obviously distinguished feature is that these cosmography parameters are free of any gravity theories and cosmological models. And Gaussian process is independent of any specific parameterized forms of function. Thus by transformations these generic cosmography parameters can be used to constrain a cosmological model and dark energy model directly at the kinematics level of our Universe. As a result, a series of cosmography parameters up to the fifth oder, i.e. the Hubble parameter H ( z ), the deceleration parameter q ( z ), the jerk parameter j ( z ), the snap parameter s ( z ) and the lerk parameter l ( z ), evolve with respect to the redshift z are reconstructed from the cosmic observations which include the recently released Pantheon+ SN Ia samples and the observational Hubble data H ( z ), also dubbed as cosmic chronometers. The result shows the transition redshift from a decelerated expansion to an accelerated expansion z t = 0 . 652 - 0.043 + 0.054 which is consistent with the previous results.
One of the most significant discoveries in modern cosmology is that the universe is currently in a phase of accelerated expansion after a switch from a decelerated expansion. The redshift corresponding to this epoch is commonly referred to as the transition redshift [Formula: see text]. In this work, we put constraints on the transition redshift with both model-independent and model-dependent approaches. We consider the recently compiled database of 32 Hubble parameter measurements and the Pantheon sample of Type Ia Supernovae (SNe). In order to include the possible systematic effects in this analysis, we use the full covariance matrix of systematic uncertainties for the Hubble parameter measurements. We plot a Hubble Phase Space Portrait (HPSP) between [Formula: see text] and [Formula: see text] in a model-independent way. From this HPSP diagram, we estimate the transition redshift as well as the current value of the equation of state parameter [Formula: see text] in a model-independent way. By considering H(z) measurements, we find the best fit value of [Formula: see text] and [Formula: see text]. We obtain the best fit value of [Formula: see text] and [Formula: see text] using the Pantheon database. Further, we also use a model-dependent approach to determine [Formula: see text]. Here, we consider a nonflat [Formula: see text]CDM model as a background cosmological model. We reconstruct the cosmic triangle plot among [Formula: see text], [Formula: see text] and [Formula: see text] where the constraints of each parameter are determined by the location in this triangle plot. By using [Formula: see text] and [Formula: see text] values, we find the best value of the transition redshift [Formula: see text], which is in good agreement with the Planck 2018 results at [Formula: see text] confidence level. We also simulate the observed Hubble parameter measurements in the redshift range [Formula: see text] and perform the same analysis to estimate the transition redshift.
The dark energy from virtual gravitons is consistent with observational data on supernovas with the same accuracy as the ΛCDM model. The fact that virtual gravitons are capable of producing a de Sitter accelerated expansion of the FLRW universe was established in 2008 (see references). The combination of conformal non-invariance with zero rest mass of gravitons (unique properties of the gravitational field) leads to the appearance of graviton dark energy in a mater-dominated era; this fact explains the relatively recent appearance of the dark energy and answers the question “Why now?”. The transition redshifts (where deceleration is replaced by acceleration) that follow from the graviton theory are consistent with model-independent transition redshifts derived from observational data. Prospects for testing the GCDM model (the graviton model of dark energy where G stands for gravitons) and comparison with the ΛCDM model are discussed.
This work aims to study the bouncing universe under [Formula: see text] theory of gravity (where [Formula: see text] and [Formula: see text] are the Gauss–Bonnet invariance and trace of energy–momentum tensor, respectively). We construct modified field equations (MFEs) to analyze the behavior of Hubble parameter (HP) for [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text] are constant terms. Different constraints are applied, engaging HP to examine the accelerating universe and to test initial singularity. The graphical analysis is made for different values of [Formula: see text] to explain bouncing process more precisely with respect to cosmic time that also provides an indication of null energy condition (NEC) violation. Resultantly, all mandatory conditions are fulfilled indicating that our proposed model provides good bouncing solutions.
In this work, by assuming a spatially flat Universe, we have tested 8 kinematic parametrization models with H ( z ) data from Cosmic Chronometers and SNe Ia from Pantheon compilation. Our aim is obtain the current values for the Hubble constant ( H 0 ), deceleration parameter ( q 0 ), jerk ( j 0 ) and snap ( s 0 ) parameters independently from a dynamical model. By using a Bayesian model comparison, three models are favoured: a model with the deceleration parameter ( q ) linearly dependent on the redshift, q linearly dependent on the scale factor and a model with a constant jerk. The model with constant jerk is slightly favoured by this analysis, furnishing H 0 = 68 . 8 - 3.6 + 3.7 km/s/Mpc, q 0 = - 0.58 ± 0.13 , j 0 = 1 . 15 - 0.53 + 0.56 and s 0 = - 0 . 25 - 0.30 + 0.40 . The other models are compatible with the constant jerk model, except for the snap parameter, where we have found s 0 = 4 . 0 - 3.0 + 3.4 for the model with q linearly dependent on the scale factor.
In this paper, we have investigated a very natural question regarding the dynamics of the universe, namely, the possibility of its decelerating phase immediately after the present accelerating phase. To begin with, we have focused on the matter creation theory which is considered to be a viable alternative to dark energy and modified gravity models. Moreover, we have introduced the cosmographic approach which allows us to express the free parameters of a cosmological model in terms of the known cosmographic parameters. Assuming a generalized matter creation rate, we have discussed the theoretical bounds on the model parameters allowing the future deceleration of the universe. Moreover, using the observational bounds on the cosmographic parameters obtained from the low redshifts observational probes, we have also examined the chance of a decelerating phase of the universe. Finally, considering a variety of known cosmological models and parametrizations, we have tested the same possibility. Our analysis shows that the chance of a future decelerating expansion of the universe is highly dependent on the choice of the cosmological models and parametrizations and also on the observational data. Even though the future decelerating expansion is allowed in some cosmological frameworks, but we do not see any strong evidence in favor of this. Perhaps, the future cosmological surveys could offer some more information regarding the fate of the universe.
This article discusses a dark energy cosmological model in the standard theory of gravity - general relativity with a broad scalar field as a source. Exact solutions of Einstein’s field equations are derived by considering a particular form of deceleration parameter , which shows a smooth transition from decelerated to accelerated phase in the evolution of the universe. The external datasets such as Hubble () datasets, Supernovae (SN) datasets, and Baryonic Acoustic Oscillation (BAO) datasets are used for constraining the model par parameters appearing in the functional form of . The transition redshift is obtained at for the combined data set (), where the model shows signature-flipping and is consistent with recent observations. Moreover, the present value of the deceleration parameter comes out to be and the jerk parameter (close to 1) for the combined datasets, which is compatible as per Planck2018 results. The analysis also constrains the omega value i.e., for the smooth evolution of the scalar field EoS parameter. It is seen that energy density is higher for the effective energy density of the matter field than energy density in the presence of a scalar field. The evolution of the physical and geometrical parameters is discussed in some details with the model parameters’ numerical constrained values. Moreover, we have performed the state-finder analysis to investigate the nature of dark energy.
In this paper, we reconstruct the late-time cosmological dynamics using a purely kinematic approach. In particular, considering a divergence-free parametrization for deceleration parameter [Formula: see text], we first derive the jerk parameter [Formula: see text] and then confront it with combination of various cosmological datasets. We use the most recent observational datasets consisting of the 1048 Pantheon Supernovae Ia data points in the redshift range [Formula: see text], the 51 data points of observational Hubble parameter (OHD) measurements in the redshift range [Formula: see text], the Hubble constant [Formula: see text] (R19) and the CMB shift parameter measurements. We study the evolution of different cosmological quantities for the present model and compare it with the concordance [Formula: see text]CDM model. We find that only the combined Pantheon+OHD+R19 data shows good agreement with the [Formula: see text]CDM [Formula: see text] model within [Formula: see text] confidence region. We also find that our model successfully generates late time cosmic acceleration along with a decelerated expansion in the past.
We quantify the evidence for cosmic acceleration using simulations of H(z) measurements from SKA- and Euclid-like surveys. We perform a non-parametric reconstruction of the Hubble parameters and its derivative to obtain the deceleration parameter q(z) using the Gaussian Processes method. This is a completely model-independent approach, so we can determine whether the Universe is undergoing accelerated expansion regardless of any assumption of a dark energy model. We find that Euclid-like and SKA-like band 1 surveys can probe cosmic acceleration at over 3 and 5σ confidence level, respectively. By combining them with an SKA-like band 2 survey, which reaches lower redshift ranges, the evidence for a current accelerated phase increases to over 7σ. This is a significant improvement from current H(z) measurements from cosmic chronometers and galaxy redshift surveys, showing that these surveys can underpin cosmic acceleration in a model-independent way.
We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of , larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter , jerk parameter and transition redshift (at which the expansion of the universe switches from being decelerated to accelerated) with errors ( confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard CDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z).
We study the performance of the latest H(z) data in constraining the cosmological parameters of different cosmological models, including that of Chevalier-Polarski-Linder parametrization. First, we introduce a statistical procedure in which the chi-square estimator is not affected by the value of the Hubble constant. As a result, we find that the H(z) data do not rule out the possibility of either non-flat models or dynamical dark energy cosmological models. However, we verify that the time varying equation of state parameter w(z) is not constrained by the current expansion data. Combining the H(z) and the Type Ia supernova data we find that the H(z)/SNIa overall statistical analysis provides a substantial improvement of the cosmological constraints with respect to those of the H(z) analysis. Moreover, the parameter space provided by the H(z)/SNIa joint analysis is in a very good agreement with that of Planck 2015, which confirms that the present analysis with the H(z) and SNIa probes correctly reveals the expansion of the Universe as found by the team of Planck. Finally, we generate sets of Monte Carlo realizations in order to quantify the ability of the H(z) data to provide strong constraints on the dark energy model parameters. The Monte Carlo approach shows significant improvement of the constraints, when increasing the sample to 100 H(z) measurements. Such a goal can be achieved in the future, especially in the light of the next generation of surveys.
As evidenced by a great number of works in the literature, it is common practice to assume that the universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the ΛCDM cosmology, or extensions thereof. On the other hand, when data is fitted to models with a time-varying dark energy equation-of-state, it turns out that such models may accommodate a non-flat universe. Several authors caution that if the assumption of spatial flatness is wrong, it could greatly hinder our understanding of dark energy, even if the curvature is in reality very small. We thus consider a number of different dynamical dark energy models that represent the complete cosmological scenario, and investigate the effects of spatial curvature on the evolution. We find that for a closed universe, the transition to the epoch of decelerated expansion would be delayed with respect to the flat case. So would the start of the current dark energy-dominated era. This would be accompanied by a larger inflationary acceleration, as well as a larger subsequent deceleration. The opposite behavior is observed if the universe is open.
We discuss Noether symmetry approach in the modified theory of gravity with Gauss-Bonnet (GB) interaction-f(G) including an ideal fluid in Friedmann-Lemaître-Robertson-Walker (FLRW) background. It yields functional form of f(G) from the symmetry. The existence of Noether symmetry gives the scale factor in two cases, but these are not satisfied by field equations in general. In another case, the solution of field equations shows late-time transition to an accelerating expansion when matter is dust, however the solution including dust and radiation is always in accelerating era.
We derive a flow of particles corresponding to Bayes’ rule that describes the big bang with both inflation and late time cosmic acceleration. In our theory the physical cause of late time cosmic acceleration is the cooling of the cosmos, which makes the measurements in Bayes’ rule much more accurate. The early cosmos was extremely hot, making measurements essentially worthless. This explains why the cosmos is accelerating now but not in roughly the first half of its existence. We derive a PDE for this flow using a log-homotopy from the prior probability density to the posteriori probability density. We derive a simple back-of-the-envelope formula for the normalized deceleration of the cosmos vs. cosmic redshift that is in excellent agreement with the latest cosmological data.
In the modified theory of gravity, the equivalence of or or interaction with an ideal fluid in Friedmann–Lemaitre–Robertson–Walker background reduces the field equations to a set of second order equations in terms of density and pressure p of the fluid with . The second order equations yield the evolution identical to the solution obtained from higher derivative gravity. The universe is radiation dominated at sufficiently large densities, while at smaller densities it is accelerating. The term also shows a deSitter solution.
Many schemes have been proposed to define a model-independent constraint on cosmological dynamics, such as the nonparametric dark energy equation of state ω(z) or the deceleration parameter q(z). These methods usually contain derivatives with respect to observational data with noise. However, there can be large uncertainties when one estimates values with numerical differentiation, especially when noise is significant. We introduce a global numerical differentiation method, first formulated by Reinsch, which is smoothed by cubic spline functions, and apply it to the estimation of the transition redshift zt with a simulated expansion rate E(z) based on observational Hubble parameter data. We also discuss some deficiencies and limitations of this method.
Distance measurements are currently the most powerful tool to study the
expansion history of the universe without specifying its matter content nor any
theory of gravitation. Assuming only an isotropic, homogeneous and flat
universe, in this work we introduce a model-independent method to reconstruct
directly the deceleration function via a piecewise function. Including a
penalty factor, we are able to vary continuously the complexity of the
deceleration function from a linear case to an arbitrary (n+1)-knots spline
interpolation. We carry out a Monte Carlo analysis to determine the best
penalty factor, evaluating the bias-variance trade-off, given the uncertainties
of the SDSS-II and SNLS supernova combined sample (JLA), compilations of baryon
acoustic oscillation (BAO) and H(z) data. We show that, evaluating a single
fiducial model, the conclusions about the bias-variance ratio are misleading.
We determine the reconstruction method in which the bias represents at most
of the total uncertainty. In all statistical analyses, we fit the
coefficients of the deceleration function along with four nuisance parameters
of the supernova astrophysical model. For the full sample, we also fit
and the sound horizon at the drag redshift. The bias-variance
trade-off analysis shows that, apart from the deceleration function, all other
estimators are unbiased. Finally, we apply the Ensemble Sampler Markov Chain
Monte Carlo (ESMCMC) method to explore the posterior of the deceleration
function up to redshift 1.3 (using only JLA) and 2.3 (JLA+BAO+H(z)). We
obtain that the standard cosmological model agrees within level with
the reconstructed results in the whole studied redshift intervals. Since our
method is calibrated to minimize the bias, the error bars of the reconstructed
functions are a good approximation for the total uncertainty.
Standard cosmological models based on general relativity (GR) with dark energy predict that the Universe underwent a transition
from decelerating to accelerating expansion at a moderate redshift zacc ∼ 0.7. Clearly, it is of great interest to directly measure this transition in a model-independent way, without the assumption
that GR is the correct theory of gravity. We explore to what extent supernova (SN) luminosity distance measurements provide
evidence for such a transition: we show that, contrary to intuition, the well-known ‘turnover’ in the SN distance residuals
Δμ relative to an empty (Milne) model does not give firm evidence for such a transition within the redshift range spanned
by SN data. The observed turnover in that diagram is predominantly due to the negative curvature in the Milne model, not the deceleration predicted by Λ cold dark matter and relatives. We show that there are several advantages in plotting distance
residuals against a flat, non-accelerating model (w = −1/3), and also remapping the z-axis to u = ln (1 + z); we outline a number of useful and intuitive properties of this presentation. We conclude that there are significant complementarities
between SNe and baryon acoustic oscillations (BAOs): SNe offer high precision at low redshifts and give good constraints on
the net amount of acceleration since z ∼ 0.7, but are weak at constraining zacc; while radial BAO measurements are probably superior for placing direct constraints on zacc.
In this article, we use observations of the Hubble parameter from the differential ages of passively evolving galaxies to constrain the New Agegraphic Dark Energy(NADE) model. The NADE is a single-parameter model. The constraint giving the best fit of the parameter is n=2.89. It is in consistent with other analyses by Hao Wei et al.( Wei, H 2007).
We study the capability of f(R) gravity models to allow for crossing the phantom boundary in both Jordan and Einstein conformal frames. In the Einstein frame, these models are equivalent to Einstein gravity with a scalar field minimally coupled to gravity. This scalar degree of freedom appears as a quintessence field with a coupling to the matter sector. We investigate the evolution of the equation of state parameter for some cosmologically viable f(R) gravity models in both conformal frames. This investigation (beyond mere theoretical arguments) acts as an operational tool to distinguish the physical status of the two conformal frames. It shows that this status is not the same.
We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200 000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with Wilkinson Microwave Anisotropy Probe (WMAP) and other data. Our results are consistent with a “vanilla” flat adiabatic cold dark matter model with a cosmological constant without tilt (ns=1), running tilt, tensor modes, or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h≈0.74-0.07+0.18 to h≈0.70-0.03+0.04, on the matter density from Ωm≈0.25±0.10 to Ωm≈0.30±0.04 (1σ) and on neutrino masses from <11 to <0.6eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the Two Degree Field Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0≈16.3-1.8+2.3Gyr to t0≈14.1-0.9+1.0Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.
We use the SnIa gold data set to compare LCDM (lambda cold dark matter) with ten representative parametrizations of the recent Hubble expansion history H(z). For the comparison we use two statistical tests: the usual χmin2 and a statistical test that we call the p-test which depends on both the value of χmin2 and the number n of parametrization parameters. The p-test measures the confidence level to which the parameter values corresponding to LCDM are excluded from the viewpoint of the parametrization tested. For example, for a linear equation of state parametrization w(z) = w0+w1z, the LCDM parameter values (w0 = −1, w1 = 0) are excluded at the 75% confidence level. We use a flat prior and Ω0m = 0.3. All parametrizations tested are consistent with the gold data set at their best fit. According to both statistical tests, the worst fits among the ten parametrizations correspond to the Chaplygin gas, the brane world and the Cardassian parametrizations. The best fit is achieved by oscillating parametrizations which can exclude the parameter values corresponding to LCDM at the 85% confidence level. Even though this level of significance does not provide a statistically significant exclusion of LCDM (it is less than 2σ) and does not by itself constitute conclusive evidence for oscillations in the cosmological expansion, when combined with similar independent recent evidence for oscillations coming from the cosmic microwave background and matter power spectra, it becomes an issue worthy of further investigation.
There is great interest in understanding a possible late accelerated expansion of the universe. Data suggest that the universe was still decelerating around redshift 1 and started to accelerate more recently at redshift 0.5. In models where the expansion is driven by a cosmological constant the acceleration should become increasingly greater with time, thus inflation never ends. This could also be the case with most models of quintessence or quintessential inflation where the late accelerated expansion is produced by a monotonically decreasing scalar potential. Here we would like to explore the possibility that a recent inflation has already or is about to end. This possibility is not ruled out by existing data and could be testable with far more, higher accuracy, supernovae on the Hubble diagram. We construct a two-stage inflationary model which can accommodate early inflation as well as a second stage of inflation (quintessence) with a single scalar field . Using an analogy from a mechanical problem we propose an inflaton field solution to the equations of motion which can account for two inflationary epochs. Inflation occurs close to the maxima of the potential. As a consequence both inflations are necesarilly finite. A first inflation is produced when fluctuations displace the inflaton field from its higher maximum rolling down the potential as in new inflation. Instead of rolling towards a global minimum the inflaton approaches a lower maximum where a second inflation takes place. The model is not realistic, however, because matter has not been taken into account at the end of the first inflation where particle production should occur as in non-oscillatory models. This is a delicate problem which will be treated elsewhere.
We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands, as part of the CFHT Legacy Survey (CFHTLS). Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z=1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multi-band photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: for a flat CDM model; and for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.
We explore the cosmological implications of an ultralight pseudo Nambu-Goldstone boson. With global spontaneous symmetry breaking scale f~=1018 GeV and explicit breaking scale comparable to Mikheyev-Smirnov-Wolfenstein neutrino masses, M~10-3 eV, such a field, which acquires a mass mphi~M2/f~H0, would currently dominate the energy density of the Universe. The field acts as an effective cosmological constant before relaxing into a condensate of nonrelativistic bosons. Such a model can reconcile dynamical estimates of the density parameter, Omegam~0.2, with a spatially flat universe, yielding H0t0~=1 consistent with limits from gravitational lens statistics.
Considerable work has been devoted to the question of how best to parametrize the properties of dark energy, in particular, its equation of state w. We argue that, in the absence of a compelling model for dark energy, the parametrizations of functions about which we have no prior knowledge, such as w(z), should be determined by the data rather than by our ingrained beliefs or familiar series expansions. We find the complete basis of orthonormal eigenfunctions in which the principal components [weights of w(z)] that are determined most accurately are separated from those determined most poorly. Furthermore, we show that keeping a few of the best-measured modes can be an effective way of obtaining information about w(z).
In conventional general relativity, the expansion rate H of a Robertson-Walker universe is related to the energy density by the Friedmann equation. Aside from the present day, the only epoch at which we can constrain the expansion history in a model-independent way is during Big-Bang Nucleosynthesis (BBN). We consider a simple two-parameter characterization of the behavior of H during BBN and derive constraints on this parameter space, finding that the allowed region of parameter space is essentially one-dimensional. We also study the effects of a large neutrino asymmetry within this framework. Our results provide a simple way to compare an alternative cosmology to the observational requirement of matching the primordial abundances of the light elements. Comment: 18 pages, Final version to be published in Phys. Rev. D
We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant. Comment: 20 pages, 6 figures
Observations of high redshift supernovae imply an accelerating Universe which can only be explained by an unusual energy component such as vacuum energy or quintessence. To assess the ability of current and future supernova data to constrain the properties of the dark energy, we allow its density to have arbitrary time-dependence, . This leads to an equation of state for the dark energy, , which is a free function of redshift z. We find that current type Ia supernova (SNe Ia) data are consistent with a cosmological constant, with large uncertainties at z\ga 0.5. We show that can be measured reasonably well to about z=1.5 using type Ia supernova data from realistic future SN Ia pencil beam surveys, provided that the weak energy condition (energy density of matter is nonnegative for any observer) is imposed. While it is only possible to differentiate between different models (say, quintessence and k-essence) at z \la 1.5 using realistic data, the correct trend in the time-dependence of the dark energy density can be clearly detected out to z=2, even in the presence of plausible systematic effects. This would allow us to determine whether the dark energy is a cosmological constant, or some exotic form of energy with a time-dependent density. Comment: final version to appear in ApJ, 552, May 10 (2001)
This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.
NB: The author will not update this review anymore, however, some of its topics are subject of other reviews. In May 2008, the article was republished in the revised Living Reviews layout, therefore the pagination has changed. The publication number lrr-2001-1 has not been altered.
We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of General Relativity of the form , with . This eliminates the need for dark energy, though it does not address the cosmological constant problem. Since a modification to the Einstein-Hilbert action of the form , with , can lead to early-time inflation, our proposal provides a unified and purely gravitational origin for the early and late time accelerating phases of the Universe. Comment: 4 pages, 1 figure, RevTeX. Typos corrected, references updated
Determination of the expansion and acceleration history of the universe is one of the fundamental goals of cosmology. Detailed measurements of these rates as a function of redshift can provide new physical insights into the nature and evolution of the dark energy, which apparently dominates the global dynamics of the universe at the present epoch. We present here dimensionless coordinate distances y(z) to twenty radio galaxies reaching out to z of about 1.8, the redshift range currently not covered by Supernova standard candle observations. We develop a simple numerical method for a direct determination of the expansion and acceleration rates, E(z) and q(z), from the data, which makes no assumptions about the underlying cosmological model or the equation of state parameter w. This differential method is in contrast to the traditional cosmological tests, where particular model equations are integrated and then compared with the observations. The new model-independent method is applied to currently available Supernova data and the data on radio galaxies presented here. We derive the expansion rate of the universe as a function of redshift, E(z), and for the first time obtain a direct estimate of the acceleration rate of the universe as a function of redshift, q(z), in a way that is independent of assumptions regarding the dark energy and its redshift evolution. The current observations indicate that the universe transitions from acceleration to deceleration at a redshift greater than 0.3, with a best fit estimate of about 0.45; this transition redshift and our determinations of E(z) are broadly in agreement with the currently popular Friedmann-Lemaitre cosmology with Omega = 0.3, and Lambda = 0.7, even though no model assumptions are made in deriving the fits for E(z) and q(z). Comment: 30 pages, 9 figures, to appear in ApJ, v597, Nov. 1, 2003
We examine the possibility that a significant component of the energy density of the universe has an equation-of-state different from that of matter, radiation or cosmological constant (). An example is a cosmic scalar field evolving in a potential, but our treatment is more general. Including this component alters cosmic evolution in a way that fits current observations well. Unlike , it evolves dynamically and develops fluctuations, leaving a distinctive imprint on the microwave background anisotropy and mass power spectrum. Comment: revised version, with added references, to appear in Phys. Rev. Lett. (4 pages Latex, 2 postscript figures)
We have discovered 16 Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to provide the first conclusive evidence for cosmic deceleration that preceded the current epoch of cosmic acceleration. These objects, discovered during the course of the GOODS ACS Treasury program, include 6 of the 7 highest-redshift SNe Ia known, all at z>1.25, and populate the Hubble diagram in unexplored territory. The luminosity distances to these and 170 previous SNe Ia are provided. A purely kinematic interpretation of the SN Ia sample provides evidence at the > 99% confidence level for a transition from deceleration to acceleration or similarly, strong evidence for a cosmic jerk. Using a simple model of the expansion history, the transition between the two epochs is constrained to be at z=0.46 +/- 0.13. The data are consistent with the cosmic concordance model of Omega_M ~ 0.3, Omega_Lambda~0.7 (chi^2_dof=1.06), and are inconsistent with a simple model of evolution or dust as an alternative to dark energy. For a flat Universe with a cosmological constant. When combined with external flat-Universe constraints we find w=-1.02 + 0.13 - 0.19 (and w_0$, and its time evolution, dw/dz, are a factor of ~8 more precise than its first estimate and twice as precise as those without the SNe Ia discovered with HST. Our constraints are consistent with the static nature of and value of w expected for a cosmological constant (i.e., w_0 = -1.0, dw/dz = 0), and are inconsistent with very rapid evolution of dark energy. We address consequences of evolving dark energy for the fate of the Universe.
We present a method for measuring the cosmic expansion history H(z) in uncorrelated redshift bins, and apply it to current and simulated type Ia supernova data assuming spatial flatness. If the matter density parameter Omega_m can be accurately measured from other data, then the dark energy density history X(z)=rho_X(z)/rho_X(0) can trivially be derived from this expansion history H(z). In contrast to customary ``black box'' parameter fitting, our method is transparent and easy to interpret: the measurement of H(z)^{-1} in a redshift bin is simply a linear combination of the measured comoving distances for supernovae in that bin, making it obvious how systematic errors propagate from input to output. We find the Riess et al. (2004) ``gold'' sample to be consistent with the ``vanilla'' concordance model where the dark energy is a cosmological constant. We compare two mission concepts for the NASA/DOE Joint Dark Energy Mission (JDEM), the Joint Efficient Dark-energy Investigation (JEDI), and the Supernova Accelaration Probe (SNAP), using simulated data including the effect of weak lensing (based on numerical simulations) and a systematic bias from K-corrections. Estimating H(z) in seven uncorrelated redshift bins, we find that both provide dramatic improvements over current data: JEDI can measure H(z) to about 10% accuracy and SNAP to 30-40% accuracy. Comment: 7 pages, 4 color figures. Expanded and revised version; PRD in press
Understanding of the nature of dark energy, which appears to drive the expansion of the universe, is one of the central problems of physical cosmology today. In an earlier paper [Daly & Djorgovski (2003)] we proposed a novel method to determine the expansion rate and the deceleration parameter in a largely model-independent way, directly from the data on coordinate distances. Here we expand this methodology to include measurements of the pressure of dark energy, its normalized energy density, and the equation of state parameter as functions of redshift. We then apply this methodology to a new, combined data set of distances to supernovae and radio galaxies. Comment: 27 pages, 8 figures. Will appear in the Astrophysical Journal, v612, September 10, 2004
Understanding the physical nature of the dark energy which appears to drive the accelerated expansion of the unvierse is one of the key problems in physics and cosmology today. This important problem is best studied using a variety of mutually complementary approaches. Daly and Djorgovski (2003, 2004) proposed a model independent approach to determine a number of important physical parameters of the dark energy as functions of redshift directly from the data. Here, we expand this method to include the determinations of its potential and kinetic energy as functions of redshift. We show that the dark energy potential and kinetic energy may be written as combinations of the first and second derivatives of the coordinate distance with respect to redshift. We expand the data set to include new supernova measurements, and now use a total of 248 coordinate distances that span the redshift range from zero to 1.79. First and second derivatives of the coordinate distance are obtained as functions of redshift, and these are combined to determine the potential and kinetic energy of the dark energy as functions of redshift. An update on the redshift behavior of the dimensionless expansion rate E(z), the acceleration rate q(z), and the dark energy pressure p(z), energy density f(z), and equation of state w(z) is also presented. We find that the standard Omega = 0.3 and Lambda = 0.7 model is in an excellent agreement with the data. We also show tentative evidence that the Cardassian and Chaplygin gas models in a spatially flat universe do not fit the data as well.
Some analyzes of the apparent magnitude‐redshift data of type Ia supernovas indicate that the suspected dark energy in the universe cannot be regarded as a cosmological constant of general relativistic origin or as the vacuum energy encountered in quantum field theories. If this is the case, our knowledge of the physical world remains deficient since no tested theory involves such a dark energy. Under this circumstance, an equation of state of the form p = wρ is not well‐motivated and one is unable to use the Einstein equation in this case as well. I argue that the very method of analysing the data by assuming exotic energy densities with strange equations of state itself is misleading and the reasonable remaining option is to make a model‐independent analysis of SNe data, without reference to the energy densities. In this basically kinematic approach, we limit ourselves to the observationally justifiable assumptions of homogeneity and isotropy, i.e., to the assumption that the universe has a RW metric. This cosmographic approach is historically the original one in cosmology. The analysis was performed by expanding the scale factor into a fifth‐order polynomial, an assumption that can be further generalized to any order. The values obtained for the present expansion rates h, q
0, r
0 etc. are relevant, since any cosmological solution would ultimately need to explain them.
Using this method, we address an important question relevant to cosmology: Was there a decelerating past for the universe? To answer this, the Bayes’s probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out models which were always accelerating from those which decelerated for at least some time in the period of interest. Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. It is argued that the lessons learned using Bayesian theory are extremely valuable to avoid frequent U‐turns in cosmology.
In this paper, using a significantly improved version of the model-independent, cosmographic approach to cosmology (John, M. V. 2004, ApJ, 614, 1), we address an important question: Was there a decelerating past for the universe? To answer this, the Bayes's probability theory is employed, which is the most appropriate tool for quantifying our knowledge when it changes through the acquisition of new data. The cosmographic approach helps to sort out the models in which the universe was always accelerating from those in which it decelerated for at least some time in the period of interest. Bayesian model comparison technique is used to discriminate these rival hypotheses with the aid of recent releases of supernova data. We also attempt to provide and improve another example of Bayesian model comparison, performed between some Friedmann models, using the same data. Our conclusion, which is consistent with other approaches, is that the apparent magnitude-redshift data alone cannot discriminate these competing hypotheses. We also argue that the lessons learnt using Bayesian theory are extremely valuable to avoid frequent U-turns in cosmology. Comment: Accepted for publication in The Astrophysical Journal (ApJ)
Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.
Models of structure formation with a cosmological constant Î provide a good fit to the observed power spectrum of galaxy clustering. However, they suffer from several problems. Theoretically, it is difficult to understand why the cosmological constant is so small in Planck units. Observationally, while the power spectra of cold dark matter plus Î models have approximately the right shape, the COBE-normalized amplitude for a scale-invariant spectrum is too high, requiring galaxies to be antibiased relative to the mass distribution. Attempts to address the first problem have led to models in which a dynamical field supplies the vacuum energy, which is thereby determined by fundamental physics scales. We explore the implications of such dynamical Î models for the formation of large-scale structure. We find that there are dynamical models for which the amplitude of the COBE-normalized spectrum matches the observations. We also calculate the cosmic microwave background anisotropies in these models and show that the angular power spectra are distinguishable from those of standard cosmological constant models. {copyright} {ital 1997} {ital The American Physical Society}
A modification to the Friedmann–Robertson–Walker equation is proposed in which the universe is flat, matter dominated, and accelerating. An additional term, which contains only matter or radiation (no vacuum contribution), becomes the dominant driver of expansion at a late epoch of the universe. During the epoch when the new term dominates, the universe accelerates; we call this period of acceleration the Cardassian era. The universe can be flat and yet consist of only matter and radiation, and still be compatible with observations. The energy density required to close the universe is much smaller than in a standard cosmology, so that matter can be sufficient to provide a flat geometry. The new term required may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher-dimensional universe. The Cardassian model survives several observational tests, including the cosmic background radiation, the age of the universe, the cluster baryon fraction, and structure formation.
We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a nontrivial minimum. For theories with dilatation anomaly one needs as a nontrivial “cosmon condition” that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short distance renormalization group behaviour of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.
The cosmological consequences of a pervasive, rolling, self-interacting, homogeneous scalar field are investigated. A number of models in which the energy density of the scalar field red-shifts in a specific manner are studied. In these models the current epoch is chosen to be scalar-field dominated to agree with dynamical estimates of the density parameter, ..cap omega../sub dyn/approx.0.2, and zero spatial curvature. The required scalar-field potential is ''nonlinear'' and decreases in magnitude as the value of the scalar field increases. A special solution of the field equations which is an attractive, time-dependent, fixed point is presented. These models are consistent with the classical tests of gravitation theory. The Eoetvoes-Dicke measurements strongly constrain the coupling of the scalar field to light (nongravitational) fields. Nucleosynthesis proceeds as in the standard hot big-bang model. In linear perturbation theory the behavior of baryonic perturbations, in the baryon-dominated epoch, do not differ significantly from the canonical scenario, while the presence of a substantial amount of homogeneous scalar-field energy density at low red-shifts inhibits the growth of perturbations in the baryonic fluid. The energy density in the scalar field is not appreciably perturbed by nonrelativistic gravitational fields, either in the radiation-dominated, matter-dominated, or scalar-field-dominated epochs. On the basis of this effect, we argue that these models could reconcile the low dynamical estimates of the mean mass density with the negligibly small spatial curvature preferred by inflation.
Recent cosmological observations strongly suggest that the Universe is dominated by an unknown form of energy with negative pressure. Why is this dark energy density of order the critical density today? We propose that the dark energy has periodically dominated in the past so that its preponderance today is natural. We illustrate this paradigm with a model potential and show that its predictions are consistent with all observations.
We argue for a ``parametrized post-Friedmanian'' approach to linear cosmology, where the history of expansion and perturbation growth is measured without assuming that the Einstein Field Equations hold. As an illustration, a model-independent analysis of 92 type Ia supernovae demonstrates that the curve giving the expansion history has the wrong shape to be explained without some form of dark energy or modified gravity. We discuss how upcoming lensing, galaxy clustering, cosmic microwave background and Lyman alpha forest observations can be combined to pursue this program, which generalizes the quest for a dark energy equation of state, and forecast the accuracy that the proposed SNAP satellite can attain. Comment: Replaced to match accepted PRD version. References and another example added, section III omitted since superceded by astro-ph/0207047. 11 PRD pages, 7 figs. Color figs and links at http://www.hep.upenn.edu/~max/gravity.html or from max@physics.upenn.edu
We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. It may also have a qualitative connection with the dS/CFT conjecture.
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and the other is an estimator that is a minimum-variance weighted quadratic function of the data. Applied iteratively, the quadratic estimator is not distinct from likelihood analysis, but is rather a rapid means of finding the power spectrum that maximizes the likelihood function. Our results bear this out: direct evaluation and quadratic estimation converge to the same C_ls. The quadratic estimator can also be used to directly determine cosmological parameters and their uncertainties. While the two methods both require O(N^3) operations, the quadratic is much faster, and both are applicable to datasets with arbitrary chopping patterns and noise correlations. We also discuss approximations that may reduce it to O(N^2) thus making it practical for forthcoming megapixel datasets. Comment: 23 Pages, 16 Figures. Final published version
The inflationary prediction of a flat Universe is at odds with current determinations of the matter density (Omega_M~0.2-0.4). This dilemma can be resolved if a smooth component contributes the remaining energy density (Omega_X=1-Omega_M). We parameterize the smooth component by its equation of state, p_X=w rho_X, and show that xCDM with w~-0.6, Omega_M~0.3 and h~0.7 is the best fit to all present cosmological data. Together, the position of the peak in the CMB angular power spectrum and the Type Ia supernova magnitude-redshift diagram provide a crucial test of xCDM. Comment: 5 pages, RevTeX, with 5 postscript figures included. Minor modifications to reflect version accepted by Phys. Rev. D
Assuming only a homogeneous and isotropic universe and using both the 'Gold'
Supernova Type Ia sample of Riess et al. and the results from the Supernova
Legacy Survey, we calculate the Bayesian evidence of a range of different
parameterizations of the deceleration parameter. We consider both spatially
flat and curved models. Our results show that although there is strong evidence
in the data for an accelerating universe, there is little evidence that the
deceleration parameter varies with redshift.
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