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The dark energy equation of state
Abstract
We perform a study of cosmic evolution with an equation of state parameter by selecting a phenomenological Λ model of the form, . This simple proposition explains both linearly expanding and inflationary universes with a single set of equation. We note
that the inflation leads to a scaling in the equation of state parameter, ω(t), and hence in equation of state. In this approach, one of its two parameters has been pin pointed and the other has been
delineated. It has been possible to show a connection between dark energy and Higgs–Boson.
... Refs. [4] and [5] discuss the concept of an oscillatory Universe from a different perspective, a dynamic dark-energy equation of state. This process would continue indefinitely without violating any known conservation laws. ...
... The best physical interpretation of the resulting model appears to be the signature change discussed in Sec. 3 simply because the outcome complements the various models in Refs. [1,2,3,4,5,6,7]. ...
... This outcome is is very much in line with the various models in Refs. [1,2,3,4,5,6,7]. An important additional feature of the embedding space is the extra timelike dimension during the decelerating phase. ...
The idea of an oscillating Universe has remained a topic of interest even after the discovery of dark energy. This paper confirms this idea by means of another well-established theory in general relativity, the embedding of curved spacetimes in higher-dimensional flat spacetimes: an n-dimensional Riemannian space is said to be of embedding class m if m+n is the lowest dimension of the flat space in which the given space can be embedded; here . So a four-dimensional Riemannian space is of class two and can therefore be embedded in a six-dimensional flat space. A line element of class two can be reduced to a line element of class one by a suitable coordinate transformation. The extra dimension can be either spacelike or timelike, leading to accelerating and decelerating expansions, respectively. Accordingly, it is proposed in this paper that the free parameter occurring in the transformation be a periodic function of time. The result is a mathematical model that can be interpreted as a periodic change in the signature of the embedding space. This signature change may be the best model for an oscillating Universe and complements various models proposed in the literature.
... The first three parameters are the matter density of the universe, Ω m , the dark energy density of the universe, Ω Λ and the radiation and relic neutrinos, Ω k . A constrain is involved when dealing with these three parameters, which is Ω m + Ω Λ + Ω k = 1 [Genovese et al., 2009, Tripathi et al., 2017, Usmani et al., 2008. The final two parameters are, respectively, the present value of the dark energy equation, w 0 , and the Hubble constant, h 0 . ...
... The final two parameters are, respectively, the present value of the dark energy equation, w 0 , and the Hubble constant, h 0 . A common assumption involves a flat universe, leading to Ω k = 0, as shown in Tripathi et al. [2017], Usmani et al. [2008]. As a result, (13) simplifies and in particular E(z) can be written as E(z) = Ω m (1 + z) 3 + (1 − Ω m )e 3 z 0 dln(1+z )[1+w(z )] , where we note that Ω Λ = 1 − Ω m . ...
... Another common assumption relies on w being constant; in this case w = w 0 . We note that several parametrizations have been proposed for the EoS (see for example Huterer and Turner [2001], Wetterich [2004] and Usmani et al. [2008]). For the present example, ground-truth parameters are set as follows: Ω m = 0.3, Ω k = 0, w 0 = −1.0 and h 0 = 0.7. ...
Approximate Bayesian computation (ABC) and synthetic likelihood (SL) are strategies for parameter inference when the likelihood function is analytically or computationally intractable. In SL, the likelihood function of the data is replaced by a multivariate Gaussian density for summary statistics compressing the observed data. While SL is conceptually simpler to implement compared with ABC, it requires simulation of many replicate datasets at every parameter value considered by a sampling algorithm, such as MCMC, making the method very computationally-intensive. We propose two strategies to alleviate the computational burden imposed by SL algorithms. We first introduce a novel adaptive MCMC algorithm for SL where the proposal distribution is sequentially tuned. Second, we exploit existing strategies from the correlated particle filters literature, to improve the MCMC mixing in a SL framework. Additionally, we show how to use Bayesian optimization to rapidly generate promising starting values for SL inference. Our combined goal is to provide ways to make the best out of each expensive MCMC iteration when using synthetic likelihoods algorithms, which will broaden the scope of these methods for complex modeling problems with costly simulators. To illustrate the advantages stemming from our framework we consider three benchmarking examples, including estimation of parameters for a cosmological model.
... • The rate of expansion in the model is continuously increasing. The Hubble's Parameter H is a function of time t which is directly proportional to t in our model whereas it is inversely proportional to time t in most of the results of [50][51][52] etc. We observed that the rate of expansion in our model is continuously increasing with time t. ...
... are constants of integration. In view of this, we have solved the equation(50). ...
... is given by The Hubble's parameter H is directly proportional to time t in our model whereas it is inversely proportional to time t occurring in the most of the works of[50][51][52] etc. It is increasing continuously with time so that the rate of expansion in the model is continuously increasing. ...
We have derived FLRW line-element in Bimetric Theory of Gravitation (BTG) by solving Rosen’s field equations, and it is concluded that the geometry of our model in BTG is agreed with the geometry of FLRW model in GR. It is also realized that for the large value of t, the deceleration parameter q in our model admits the value which is close to the value at present epoch predicted by the observations of [44-48].This This shows that our FLRW model in BTG is found to be in an accelerating phase at present epoch which is not the case in GR. Other geometrical and physical aspects to the model are also studied.
... In this regard, DE EOS ω is considered to be equal to -1. Jimenez, Usmani, et al, & Amendola [10][11][12] have suggested quintessence and phantom forms of dark energies models with ω >-1 & ω< -1 respectively. Gorbunova & Timoshkin [13], and Das et al [14] have proposed theoretical models with time-dependent ω which is yet to be confirmed experimentally. ...
... Divergence of Einstein's tensor has been given by, Substituting p = ω ρ and p = (ω+δ) ρ in equation (11), it is further simplified as: ...
In this paper, we have investigated the dark energy cosmological model in the presence of anisotropic fluid in Kaluza-Klein metric with generalized time-dependent lambda Λ=αH 2 + βS 2 (α, β are free parameters; H is Hubble parameter and S is normal scale factor). Considering the equation of state (EOS) p = ωρ for normal dimensions and pψ= (ω+δ)ρ for the fifth dimension, exact solutions of Einstein field equations of the anisotropic model are obtained (where p-the pressure for normal dimensions, pψ-the pressure of the fifth dimension, ρ-density of the fluid, ω-EOS parameter, and δ-skewness parameter). It is concluded that the universe at its early stage shows anisotropic behavior due to its finite value δ. The variations of ω and δ demonstrate the evolution from radiation dominated early universe to a dark energy-dominated universe. We have also investigated dark energy density, pressure, and other physical parameters. The physical parameters are dependent on free parameters and power index factor n which relates the extra dimension scale factor to the normal scale factor.
... The approach starts from an initial guess and utilizes a smoothing kernel to generate another curve closer to the data points (Shafieloo et al. 2006;Shafieloo & Clarkson 2010;Vazirnia & Mehrabi (2021). The SM has been used to reconstruct the cosmic expansion history, as well as the equation of state (EOS) of the DE in Linder (2003), Kopp et al. (2018), and Usmani et al. (2008). ...
... . It is worth noting that for a conserved DE fluid with a positive density ρ DE >0, the EOS fully determines its evolution. This is the main reason why, in lots of works, people consider the EOS instead of the density to study the evolution of the DE (Usmani et al. 2008;Lazkoz et al. 2010). However, the effective EOS can become singular in some models (Khurshudyan 2013;Solà & Štefančić 2005), and so the DE density changes its sign and could be negative. ...
The evolution of the dark energy (DE) density is a crucial quantity for understanding the nature of DE. Often, the quantity is described by the so-called equation of state; that is, the ratio of the DE pressure to its density. In this scenario, the DE density is always positive throughout cosmic history, and a negative value is not allowed. Assuming a homogeneous and isotropic universe, we reconstruct the DE density directly from observational data and investigate its evolution throughout cosmic history. We consider the latest Type Ia supernova, baryon acoustic oscillation, and cosmic chronometer data, and reconstruct the DE density in both flat and nonflat universes up to redshift z ∼ 3. The results are well in agreement with ΛCDM up to redshift z ∼ 1.5, but we see a weak sign of negative DE density at high redshifts.
... The approach starts from an initial guess and utilizes a smoothing kernel to generate another curve closer to the data points [42][43][44]. The SM method has been used to reconstruct the cosmic expansion history as well as the equation of state (EoS) of the dark energy in [45][46][47]. ...
... It is worth noting that for a conserved DE fluid with a positive density ρ DE > 0, the EoS fully determines its evolution. This is the main reason why in lots of works, people consider EoS instead of density to study the evolution of the DE [47,48]. However, the effective EoS can become singular in some models [49,50] and so the DE density changes its sign and could be negative. ...
The evolution of dark energy density is a crucial quantity in understanding the nature of dark energy. Often, the quantity is described by the so-called equation of state, that is the ratio of dark energy pressure to its density. In this scenario, the dark energy density is always positive throughout cosmic history and a negative value is not allowed. Assuming a homogeneous and isotropic universe, we reconstruct the dark energy density directly from observational data and investigate its evolution through cosmic history. We consider the latest SNIa, BAO and cosmic chronometer data and reconstruct the dark energy density in both flat and non-flat universes up to redshift . The results are well in agreement with the CDM up to redshift , whereas all data and methods, in our analysis, provide a negative dark energy density at high redshifts.
... Recently, Sahni and Starobinsky [36] have developed methods for restoration of the quantity ω(t) from expressional data that has been established to determine this parameter as a function of cosmological time (see Sahni et al. [37] and references there in). Recently, the parameter ω(t) is calculated with some reasoning which reduced some simple parametrization of the dependencies by some authors (Huterer and Turner [38]; Weller and Albrecht [39]; Linden and Virey [40]; Krauss et al. [41]; Usmani et al. [42]; Chen et al. [43]). The simplest DE candidate is the vaccuum energy (ω = −1), which is mathematically equivalent to the cosmological constant (Λ). ...
... state parameter in Kaluza-Klein metric and wormholes (Rahaman et al. [57,58]). In recent years, various forms of time-dependent ω have been used for variable Λ models (Mukhopadhyay et al. [59]; Usmani et al. [42]). Recently, Ray et al. [60], Akarsu and Kilinc [61,62], Yadav et al. [63], Pradhan and Amirhashchi et al. [64] and Pradhan et al. [65] have obtained DE models with variable EoS parameter. ...
Before 1998, it was usually expected that the universe was expanding with a constant rate or the expansion was slowing down. In 1998, the surprising discovery based on type Ia supernovae, that the rate of expansion of the universe is increasing, forced the researchers to reconsider the various cosmological models proposed so far. The current study is also an effort to revisit the LRS Bianchi type-II, dark energy (DE) model by taking time-dependent deceleration parameter (DP) instead of constant DP. We have assumed the variable scale factor a(t) = [sinh(αt)] 1 n, which gives the variable DP as q(t) = nsech2(αt)-1, with these considerations, the solutions of field equations are calculated. Various parameters of DE models are also calculated, and it is found that these are consistent with the recent observations.
... As evident from Fig. 1, the equation of state parameter changes with the redshift and hence is time dependent. It turns out that the above problem of time dependent equation of state parameter is equivalent to that of an interacting dark energy fluid, which has been extensively studied in [28][29][30][31][32][33][34][35][36][37]. Using Monte Carlo Markov Chain technique one can demonstrate that models involving interacting dark energy (or, time dependent equation of state parameter) has degeneracy between the matter density and the dark energy interaction rate. ...
A shift-symmetric Galileon model in presence of spacetime torsion has been constructed for the first time. This has been realized by localizing (or, gauging) the Galileon symmetry in flat spacetime in an appropriate manner. We have applied the above model to study the evolution of the universe at a cosmological scale. Interestingly, for a wide class of torsional structures we have shown that the model leads to late time cosmic acceleration. Furthermore, as torsion vanishes, our model reproduces the standard results.
... Now, before going further, we want to replaceρ in Eq. (31) byT and this can be done by choosing a particular value of the equation of state (EoS) parameter (ω) defined as,ω =p/ρ. We know that for the FLRW universe, the dark energy era has started fromω = −1/3 [91] and the present value ofω is near about −1 [81,82]. We chose the EoS parameter to bē ...
... In this way, the state parameter ω being the ratio of the pressure to the energy density describes different models depending on its value. For instance, the state parameter ω = −1 is assigned to the cosmological constant model while the case −1/3 < ω < 0 can be associated to different models, i.e quintessence or K-essence [50][51][52]. ...
In this paper, we generate a rotating solution of the reduced Kiselev black hole through the Newman-Janis formalism. Based on such solution, we remark different shadow behaviors by varying the involved parameters . Concretely, we observe that the allowed values of the spin parameter a are much less than the usual rotating black holes. By deeply analysing the shadow shapes, we show that comparable shadow shapes emerge for the same ratio . On the other hand, we recognize that the parameters a and governs the shadow geometry while the parameter rules the size of such a quantity. Besides, we notice that an elliptic shadow geometry appears for certain range of relevant parameters. By making contact with the observational side, we provide a constraint on the rotating reduced Kiselev (RRK) black hole parameters. In particular, we find a good compatibility between the theoretical and experimental results. Regarding Hawking radiation, we note that the Kiselev radius shows a similar behavior to the quintessence filed intensity . Concerning the light motion in the vicinity of a RRK black hole, we investigate deeply the deflection by varying the relevant parameters. In particular, we remark that such a quantity decreases by increasing the parameters a and while the opposite effect is observed when increasing .
... Such parameterized EoS of the DE can circumvent the selection of the potential, enabling the system to be constrained directly by the observation [17]. In this paper, we will evaluate the dynamics of the system using the parametrization de = 0 + 1 ( / ),3 [18]. To accomplish this, we will first define the minimal dimensionless dynamical variables required ...
In this paper, we present a dynamical system analysis of the tachyon dark energy model by parametrization of the equation of state (EoS) of the dark energy. The choice of parametrization can constrain the form of the field potential, and as a result, the theory can be directly constrained from the observation without assuming a particular form of the potential. 1
... Such parameterized EoS of the DE can circumvent the selection of the potential, enabling the system to be constrained directly by the observation [17]. In this paper, we will evaluate the dynamics of the system using the parametrization de = 0 + 1 ( / ),3 [18]. To accomplish this, we will first define the minimal dimensionless dynamical variables required ...
In this paper, we present a dynamical system analysis of the tachyon dark energy model by parametrization of the equation of state (EoS) of the dark energy. The choice of parametrization can constrain the form of the field potential, and as a result, the theory can be directly constrained from the observation without assuming a particular form of the potential.
... Here, we consider the parametrization studied in Refs. [52,53]. This is a completely different way of parametrizing a time-dependent EOS of the scalar field. ...
In this work, we present a new scheme to study the tachyon-dark-energy model using dynamical systems analysis by considering parametrization of the equation of state (EOS) of the dark energy. Both the canonical and phantom field dynamics are investigated. In our method, we do not require any explicit form of the tachyon potential. Instead of the potential, we start with an approximate form of the EOS of the tachyon field. This EOS is phenomenologically motivated and contains some dimensionless parameters. Using our method, we can construct the dynamical system which gives rise to the time evolution of the Universe. We have considered two different parametrizations of the EOS and studied the phase space dynamics in detail. Our analysis shows Taylor series parametrization of the EOS has serious cosmological limitations. We have also provided an example of how this method can be applied to coupled tachyon models with a specific form of interaction. Our proposal is generic in nature and can be applied to other scalar field dark energy models.
... Refs. [4] and [5] discuss the concept of an oscillatory Universe from a different perspective, a dynamic dark-energy equation of state. This process would continue indefinitely without violating any known conservation laws. ...
... motivates us to try other parametrizations for the equations of state of tachyonic dark energy. Here we consider the parametrization studied in [47,48]. This is a completely different way of parametrizing a time dependent EoS of the scalar field. ...
In this work we present a new scheme to study the tachyon dark energy model using dynamical systems analysis by considering parametrization of the equation of state(EoS) of the dark energy. Both the canonical and phantom field dynamics are investigated. In our method we do not require any explicit form of the tachyon potential. Instead of the potential we start with an approximate form of the EoS of the tachyon field. This EoS is phenomenologically motivated and contains some dimensionless parameters. Using our method we can construct the dynamical system which gives rise to the time evolution of the universe. We have considered two different parametrizations of the EoS and studied the phase space dynamics in details. Our analysis shows Taylor series parametrization of the EoS has serious cosmological limitations. Our proposal is generic in nature and can be applied to other scalar field dark energy models.
... Based on the three layer system it is now established that the theoretical acceptance of gravastar model in both lower and higher dimensions with or without charge is important in astrophysics. Usmani et al. [17] shown the possibility of existence of higher dimensional gravastar, and later on Bhar [24] and Ghosh et al. [26] studied the higher dimensional gravastar with and without conformal motion respectively. The possibility of gravastar in lower dimension is also studied [28,29]. ...
Gravastars have been considered as a feasible alternative to black holes in the past couple of decades. Stable models of gravastar have been studied in many of the alternative gravity theories besides standard General Relativity (GR). The Rastall theory of gravity is a popular alternative to GR, specially in the cosmological and astrophysical context. Here, we propose a stellar model under the Rastall gravity following Mazur-Mottola's [1, 2] conjecture. The gravastar consists of three regions, viz., (I) Interior region, (II) Intermediate shell region, and (III) Exterior region. The pressure within the interior core region is assumed with a constant negative matter-energy density which provides a repulsive force over the entire thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma which follows the Zel'dovich's conjecture of stiff fluid [3, 4]. It is also assumed that the pressure is proportional to the matter-energy density according to Zel'dovich's conjecture, which cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum which is described by the Schwarzschild-de Sitter solution. Under all these specifications we obtain a set of exact and singularity-free solutions of the gravastar model presenting several physically valid features within the framework of Rastall gravity. The physical properties of the shell region namely, the energy density, proper length, total energy and entropy are explored. The stability of the gravastar model is investigated using the surface redshift against the shell thickness and maximizing the entropy of the shell within the framework of Rastall gravity.
... Based on the three layer system it is now established that the theoretical acceptance of gravastar model in both lower and higher dimensions with or without charge is important in astrophysics. Usmani et al. [17] shown the possibility of existence of higher dimensional gravastar, and later on Bhar [24] and Ghosh et al. [26] studied the higher dimensional gravastar with and without conformal motion respectively. The possibility of gravastar in lower dimension is also studied [28,29]. ...
Gravastars have been considered as a feasible alternative to black holes in the past couple of decades. Stable models of gravastar have been studied in many of the alternative gravity theories besides standard General Relativity (GR). The Rastall theory of gravity is a popular alternative to GR, specially in the cosmological and astrophysical context. Here, we propose a stellar model under the Rastall gravity following Mazur-Mottola's \cite{Mazur2001,Mazur2004} conjecture. The gravastar consists of three regions, viz., (I) Interior region, (II) Intermediate shell region, and (III) Exterior region. The pressure within the interior core region is assumed with a constant negative matter-energy density which provides a repulsive force over the entire thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma which follows the Zel'dovich's conjecture of stiff fluid \cite{Zeldo1962,Zel'dovich1972}. It is also assumed that the pressure is proportional to the matter-energy density according to Zel'dovich's conjecture, which cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum which is described by the Schwarzschild-de Sitter solution. Under all these specifications we obtain a set of exact and singularity-free solutions of the gravastar model presenting several physically valid features within the framework of Rastall gravity. The physical properties of the shell region namely, the energy density, proper length, total energy and entropy are explored. The stability of the gravastar model is investigated using the surface redshift against the shell thickness and maximizing the entropy of the shell within the framework of Rastall gravity.
... A dynamical model with Λ = αH 2 , where HðtÞ = _ a/a, has been explored by Mukhopadhyay et al. [27]. A similar model with _ Λ ∼ H 3 has been considered in [28,29]. The main motivation of considering Λ ∼ € a/a and Λ ∼ ρ is to prove that these two dynamical models are equivalent for both open and closed universes in addition to the flat space, which has already been proved previously. ...
It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.
... The methods for restoration of the quantity ( ) t from expressional data have been developed [8], and an analysis of the experimental data has been conducted to determine this parameter as a function of cosmological time [9]. Recently the parameter ( ) t has been calculated with some reasoning which reduced to some simple parameterization of the dependences by some authors ( [10], [11], [12], [13], [14], [15]). These observations provide us a clear outline of the universe: it is flat and full of un-damped form of energy density pervading the Universe. ...
Spatially homogeneous axially symmetric cosmological models filled with barotropic fluid and dark energy are obtained in a scalar tensor theory of gravitation proposed by Brans and Dicke (1961). In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. Also some important features of the models, thus obtained, have been discussed.
... As evident from Fig. 1, the equation of state parameter changes with the redshift and hence is time dependent. It turns out that the above problem of time dependent equation of state parameter is equivalent to that of an interacting dark energy fluid, which has been extensively studied in [28][29][30][31][32][33][34][35][36][37]. Using Monte Carlo Markov Chain technique one can demonstrate that models involving interacting dark energy (or, time dependent equation of state parameter) has degeneracy between the matter density and the dark energy interaction rate. ...
A shift-symmetric Galileon model in presence of spacetime torsion has been constructed for the first time. This has been realized by localizing (or, gauging) the Galileon symmetry in flat spacetime in an appropriate manner. We have applied the above model to study the evolution of the universe at a cosmological scale. Interestingly, for a wide class of torsional structures we have shown that the model leads to late time cosmic acceleration. Furthermore, as torsion vanishes, our model reproduces the standard results.
... The methods for restoration of the quantity ω(t) from expressional data has been developed (Sahni and Starobinsky [39]), and an analysis of the experimental data has been conducted to determine this parameter as a function of cosmic time (see Sahni et al. [40] and references therein). Recently, the parameter ω(t) has been calculated with some reasoning which reduced to some simple parameterization of the dependences by some authors (Huterer and Turner [41]; Weller and Albrecht [42]; Linden and Virey [43]; Krauss et al. [44]; Usmani et al. [45]; Chen et al. [46]). The simplest DE candidate is the vacuum energy (ω = −1), which is mathematically equivalent to the cosmological constant (Λ). ...
In the present paper, we have been investigated a new dark energy model in anisotropic Bianchi-type-I (B-I) space-time with redshift-dependent equation of state (EoS) parameter. The Einstein’s field equations have been solved by applying a variation-law for hyperbolic scale factor (Formula presented.) which provides a time-dependent deceleration parameter and time-dependent EoS parameter. We also have been found the redshift-dependent EoS parameter. The existing range of the dark energy EoS parameter (Formula presented.) for derived model is found to be in good agreement with the recent observations. The cosmological constant (Formula presented.) is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is collaborated by results from recent supernovae Ia observations. It has also been suggested that the dark energy that explains the observed accelerating universe may arise due to the contribution to the vacuum energy of the EoS in a time-dependent background. Geometric and Kinematic properties of the model and the behavior of the anisotropy of the dark energy have been discussed.
... The above EOS is known in the literature as a 'false vacuum', 'degenerate vacuum', or 'ρ-vacuum' [19][20][21][22] which represents a repulsive pressure, an agent responsible for the accelerating phase of the Universe, and is termed as the -dark energy [23][24][25][26][27] . It is argued by [16] that a charged gravastar seems to be connected to the dark star [28][29][30]. ...
We explore possibility to find out a new model of gravastars in the extended D-dimensional Einstein–Maxwell space–time. The class of solutions as obtained by Mazur and Mottola of a neutral gravastar [1,2] have been observed as a competent alternative to D-dimensional versions of the Schwarzschild–Tangherlini black hole. The outer region of the charged gravastar model therefore corresponds to a higher dimensional Reissner–Nordström black hole. In connection to this junction conditions, therefore we have formulated mass and the related Equation of State of the gravastar. It has been shown that the model satisfies all the requirements of the physical features. However, overall observational survey of the results also provide probable indication of non-applicability of higher dimensional approach for construction of a gravastar with or without charge from an ordinary 4-dimensional seed as far as physical ground is concerned.
... In 2011, the latest results were obtained from a combination of cosmological data sets coming from CMBR anisotropies, luminosity distances of high red-shift type-Ia supernovas, and galaxy clustering, which constrain the DE EoS to −1.44 < ω < −0.92 at the 68% confidence level [12], [32]. Various time-dependent EoS parameters were recently used for models with a variable Λ [33], [34], and several DE models with a variable ω were recently obtained in [35] and also in [36]. ...
In this paper, we study the spatially homogeneous and totally anisotropic Bianchi
type-II cosmological models within the framework of Brans-Dicke (BD) theory
of gravity in the background of anisotropic dark energy (DE) with variable
equation of state (EoS) parameter and constant deceleration parameter. We
use a power law relation between the scalar �eld and scale factor R to �nd
the solutions. The dark energy EoS parameter ! and its existing range for the
models is in good agreement with the following recent observations:
� SNe Ia data,
� SNe Ia data + CMBR anisotropy + galaxy clustering statistics,
� combination of cosmological data sets coming from CMB anisotropy, luminosity
distances of high red-shift type Ia supernovae and galaxy clustering.
It has been observed that the cosmological constant � is decaying with time,
which is consistent with recent cosmological observations. The stability conditions
and physical features of the models have been studied.
In this study, we explore the evolution of dark energy by focusing on the gravitational sector rather than the matter source. Specifically, we examine a modified version of symmetric teleparallel gravity, known as f(Q) gravity, where the non-metricity scalar Q governs gravitational interactions. The f(Q) model investigated takes the form , incorporating both linear and nonlinear contributions to Q , with , , and n as free parameters. Using initial conditions based on CDM observational Planck 2018 data (, ), we analyze the model's behavior for various values of n . To characterize the dark energy dynamics, we employ statefinder diagnostics , , and , along with the diagnostic plane.
Our results reveal that the model exhibits both Chaplygin gas and quintessence-like behaviors in the and planes for different values of n . The diagnostic further distinguishes the f(Q) model from other dark energy frameworks, demonstrating its versatility and potential as a cosmological model. This study highlights the capacity of f(Q) gravity to provide a unified explanation of late-time cosmic acceleration, offering new insights into the nature of dark energy.
This paper explores the evolution of gravastars within the context of the Lyra geometry. The mathematical formulations of the three regions of a gravastar: (i) the inside region, (ii) the shell region and (iii) the external void region are described separately, along with their physical characteristics and graphical representations. The study explores different aspects of our model by analysing the behaviour of physical parameters. It solves the modified Einstein’s field equations, which are derived from this geometry, under the conditions of gravastar formation. The investigation focusses on the physical properties of the shell region, such as energy density, proper length, full energy, entropy, surface tension, thinness and energy conditions. Additionally, the stability of the gravastar model is examined by analysing the surface red-shift in relation to the shell length.
In this paper we attempt to construct a regular gravastar model using the UV corrected framework of Loop Quantum Cosmology.Wefindthatastablegravastarmodelcanbeconstructedwithanumberofuniquefeatures:(i)nothinshellapproximation needs to be invoked to obtain solutions in the shell which can be considered to be of a finite thickness, (ii) the central singularity of a self-gravitating object can be averted by a bounce mechanism, such that the interior density of the gravastar reaches a maximum critical density and cannot be raised further due to an operative repulsive force, (iii) the inherent isotropy of the effective fluid description does not prevent the formation of a stable gravastar, and anisotropic pressures is not an essential requirement.
We propose a class of models, in which stable gravastar with large surface redshift becomes a solution. In recent decades, gravastars have become a plausible substitute for black holes. Researchers have explored stable gravastar models in various alternative gravity theories, in addition to the conventional framework of general relativity. In this paper, we present a stellar model within the framework of Einstein's gravity with two scalar fields, in accordance with the conjecture proposed by Mazur and Mottola [Proc. Nat. Acad. Sci. 101 (2004), 9545-9550]. In the model, the two scalar fields do not propagate by imposing constraints in order to avoid ghosts. The gravastar comprises two distinct regions, namely: (a) the interior region and (b) the exterior region. We assume the interior region consists of the de Sitter spacetime, and the exterior region is the Schwarzschild one. The two regions are connected with each other by the shell region. On the shell, we assume that the metric is given by a polynomial function of the radial coordinate r. The function has six constants. These constants are fixed by the smooth junction conditions, i.e., the interior region with the interior layer of the shell and the exterior region with the exterior layer of the shell. From these boundary conditions, we are able to write the coefficients of the scalar fields in terms of the interior radius and exterior radius. To clarify the philosophy of this study, we also give two examples of spacetimes that asymptote as the de Sitter spacetime for small r and as the Schwarzschild spacetime for large r. Exploration is focused on the physical attribute of the shell region, specifically, its proper length. The gravastar model's stability has frequently been examined by analyzing the relationship between surface redshift and shell thickness, a comparison we also undertake with previous models. Especially, we show that there exists a stable gravastar with a large surface redshift prohibited by the instability in the previous works. Furthermore, by checking the effective equation of state parameters, we show that the gravastar geometry realized in this paper by using two scalar fields could be difficult to generate with ordinary fluid.
In this paper, we have extended the idea of gravitational Bose-Einstein condensate star (gravastar) to charged gravastar system and explored the role of charge in gravastar formation and its properties. We have used the most general line element in cylindrically symmetric space-time. In this approach, the existence of singularity at the center of gravastar is removed and the event horizon is replaced by the thin shell approximation. The proper length of the shell is calculated along with the energy of the thin shell in presence of charge. The entropy calculation shows that the entropy of the configuration is smaller than that of a quasi-black hole system and even smaller than that of a classical black hole. Unlike black hole, the gravastar system is a stable configuration and in our approach there is no information paradox.
The main purpose of this manuscript is to investigate the Bianchi type-I dark energy cosmological models in the framework of Lyra geometry. The modified Einstein’s field equations is derived for Lyra geometry and obtained the exact solutions. In order to obtained the exact solutions volumetric expansion law is used. As per the Exponential and Power-law expansion, we have discussed the two cosmological models. Several physical parameters are obtained for both the models and discuss its physical importance following the observational data.KeywordsBianchi type-ICosmological constantLyra geometry
One of the solutions of the Einstein equations, called McVittie solution, signifying a black hole embedded by the dynamic spacetime is studied. In the stationary spacetime the Mcvittie metric becomes the Schwarzschild‐de Sitter metric (SdS). The geodesic of a freely falling test particle towards the black hole is examined in the SdS spacetime. It is found that unlike the Schwarzschild case the potential of such particle becomes maximum at a point where it eventually stops for a while and then resumes its motion towards the center of the black hole. It is shown that an observer or system of particles is spaghettified near the black hole singularity in the SdS spacetime. The dynamics of the universe in the framework of McVittie metric, being a generalized time dependent SdS solution, is represented in terms of that point, called stationary or turning point. The motion of the stationary point is studied in various regimes of the expanding universe and the possible outcomes are discussed in brief.
We present spherically symmetric anisotropic charged strange stars under the framework of f(R,T) gravity. For this we consider that the Lagrangian density is a linear function of R and T where R is the Ricci Scalar and T represents the trace of the energy–momentum tensor. These stars are considered to be built with Strange Quark Matter (SQM) distribution. To describe this SQM distribution inside the stellar bodies, we incorporate the simplest form of phenomenological MIT bag model equation of state (EOS) pr=13(ρ−4Bg), where pr is the radial pressure, ρ is the energy density and Bg is the bag constant. To determine density and pressure from the Einstein Field Equations (EFE), we use Krori-Barua (KB) metric and using the observed values of mass and radius for strange star candidates LMCX−4, we calculate the value of Bg from our model. Comparing the interior metric with exterior Reissner-Nordström metric at the surface, we calculate the unknown parameters incorporating the observed values of the mass and radius, we find that the coupling constant χ affects the bag value significantly. The model shows consistency with all the physical conditions and presents a viable study to the nature of charged anisotropic massive stellar system.
In the current article, we study anisotropic spherically symmetric strange star under the background of f(R, T) gravity using the metric potentials of Tolman–Kuchowicz type (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) as and which are free from singularity, satisfy stability criteria and also well-behaved. We calculate the value of constants a, b, B and C using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) where the density profile () is related to the radial pressure () as . Here quark pressure is responsible for generation of bag constant . Motivation behind this study lies in finding out a non-singular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herrera’s cracking condition and also with Harrison–Zeldovich–Novikov’s static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model.
In this present article, we have proposed gravastar under Finslerian spacetime geometry, which can be claimed as an alternative to Finslerian black hole. This study can be considered as a sequel of our previous works based on the Finslerian geometry where we have constructed some phenomenological models for compact stars and wormholes. The concept of gravastar was first proposed by Mazur and Mottola (2001. arXiv:gr-qc/0109035; Proc Natl Acad Sci USA 101:9545, 2004) which consist of three regions in its configuration namely (I) the interior core, (II) the intermediate thin shell, and (III) the vacuum exterior. These three regions can be described by three different equation of state. Here we solve gravastar under the framework of Finsler geometry and obtain a set of exact and physically acceptable solutions for three different regions. We have also studied various physical parameters which are fulfilled by the physical requirement for validity of the present study on gravastar within the Finslerian spacetime geometry.
The development of gravastar model by Mazur and Mottola
(2004) is one of the most acceptable alternatives of conventional
classical black hole. They have studied phase transition of the
collapsing stellar objects at low temperature near event horizon
which leads to the condensate phase, i.e. Bose–Einstein condensation.
In the present study we have obtained a unique solution
of this gravastar model under Einstein’s GR in (3+1) dimensions
by incorporating the Karmarkar condition for embedding class
1. The most important motive of this work is to find an exact
solution of the shell without taking the thin shell approximation.
We have obtained singularity free finite solutions for the interior
of the gravastar.
In this article, we study the structure of the general relativistic thick disks in the accelerating expanding universe which is dynamically dominated by dark energy. By applying a conformal transformation on the metric of a thick disk in isotropic coordinates of a static universe, we study the disk in the Friedman-Robertson-Walker (FRW) spacetime of an expanding universe. Also, we investigate the structure of a thick disk in a dynamical state by solving Einstein equations in the presence of cosmological constant Λ. Moreover, modified mass and energy densities of the thick disk, as well as its radial, azimuthal, and vertical pressures, are examined as the functions of time. Furthermore, we check out energy conditions for the relativistic thick disks in the expanding universe.
In this article we propose a relativistic model of a static spherically symmetric
anisotropic strange star with the help of Tolman-Kuchowicz (TK) metric
potentials [Tolman, Phys. Rev. 55, 364 (1939) and Kuchowicz, Acta Phys.
Pol. 33, 541 (1968)]. The form of the potentials are �(r) = ln(1 + ar2 + br4)
and �(r) = Br2 + 2 lnC where a, b, B and C are constants which we have to
evaluate using boundary conditions. We also consider the simplest form of the
phenomenological MIT bag equation of state (EOS) to represent the strange
quark matter (SQM) distribution inside the stellar system. Here, the radial
pressure pr relates with the density pro�le � as follows, pr(r) = 1
3 [�(r)4Bg],
where Bg is the Bag constant. To check the physical acceptability and stability
of the stellar system based on the obtained solutions, we have performed
various physical tests. It is shown that the model satis�es all the stability
criteria, including nonsingular nature of the density and pressure, implies
stable nature. Here, the Bag constant for di�erent strange star candidates are
found to be (68 70) MeV/fm3 which satis�es all the acceptability criteria
and remains in the experimental range.
In the present article we are going to study different features of a Gravitationally Vacuum Condensate Star, i.e., Gravastar with the help of the Kuchowicz metric potential [B. Kuchowicz, Acta. Phys. Pol. 33, 541 (1968)] in (3+1) dimensional spacetime. The gravastar consists of three regions namely the interior, intermediate thin shell and the exterior. Our main objective is to study the non-singular solutions of the system considered here. Also we want to study different features of the shell region, composed of ultra relativistic plasma obeying Zel’dovich’s conjecture of stiff fluid, like the energy, proper length, entropy and surface redshift which will confirm the stability of our model. Using the Kuchowicz metric potential we have found another metric potential (i.e. eλ) for the interior and shell region which is non-singular in its nature for both of the region. The exterior of the gravastar has been described as the Schwarzschild type. We have found the numerical values of different constants imposing the boundary conditions. This theoretical model of gravastar can completely overcome the singularity problem related to black holes and hence can be taken as a promising alternative to the classical black hole within the framework of Einstein’s General Relativity. Keywords: General relativity, Gravastar, Kuchowicz metric potential
This paper examines the physical behaviour of the transition of the LRS Bianchi type-I perfect-fluid cosmological models from early decelerating to the current accelerating phase within the framework of the f(R,T) theory of gravity. To determine the solution of the field equations, the concept of a time-dependent deceleration parameter is used. This yields scale factors for which the universe attains a phase transition scenario, and is consistent with recent cosmological observations. Two cases are considered, firstly , where n and are positive constants. For , this generates a class of accelerating models, while for , the universe attains a phase transition from an early decelerating to the present accelerating phase. This model 1 starts from quintessence () initially and ended up with phantom phase when . The second case is , where n and k are positive constants. It is observed that for and , a class of transit models of the universe are obtained. The model 2 belongs to the scenario of phantom energy (). We have observed the existence of type-III singularity in our model 2. Some physical and geometric properties of the models are found and discussed.
We have constructed a self-consistent system of Bianchi Type VI0 cosmology, and mingling of perfect fluid and dark energy in five dimensions. The usual equation of state p=γρ with γ∈[0,1] is chosen by the perfect fluid. The dark energy assumed to be chosen is taken into consideration to be either the quintessence or Chaplygin gas. The same solutions pertaining to the corresponding the field equations of Einstein are obtained as a quadrature. State parameter’s equations for dark energy ω is found to be consistent enough with the recent observations of SNe Ia data (SNe Ia data with CMBR anisotropy) and galaxy clustering statistics. Here our models predict that the rate of expansion of Universe would increase with passage of time. The cosmological constant Λ is traced as a declining function of time and it gets nearer to a small positive value later on which is supported by the results from the current supernovae Ia observations. Also a detail discussion is made on the physical and geometrical aspects of the models.
Рассмотрен ряд анизотропных моделей темной энергии типа Бианки-II в рамках теории гравитации Бранса-Дикке с переменным параметром уравнения состояния и постоянным параметром замедления. Для получения большинства аналитических решений используется степенная связь между скалярным полем и масштабным фактором A, а также между средними значениями параметра Хаббла H и масштабного фактора A. Параметр темной энергии уравнения состояния и допустимый в модели диапазон его изменения находятся в хорошем согласии с последними данными наблюдений. Было обнаружено, что космологическая постоянная затухает со временем, что также согласуется с последними космологическими наблюдениями. Изучены динамическая устойчивость и физические особенности моделей.
We present a new model of gravastar in the higher dimensional Einstein-Maxwell spacetime including Einstein's cosmological constant . Following Mazur and Mottola~\cite{Mazur2001,Mazur2004} we obtain a set of solutions for gravastar. This gravastar is described by three different regions namely, (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact and non-singular solutions of the gravastar which seems physically very interesting and reasonable.
The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble’s parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter K occurring in the metric of the space–time. The model for K = 0 corresponds to an accelerating Universe with isotropic dark energy. The other two models for K = 1 and −1 represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.
The renormalization group (RG) approach to cosmology is an efficient method for studying the possible evolution of the cosmological parameters from the point of view of quantum field theory (QFT) in curved space time. In this work we continue our previous investigations of the RG method based on potential low-energy effects induced from physics at very high energy scales M_{\mathrm {X}}\lesssim M_{\mathrm {P}} . In the present instance we assume that both the Newton constant, G, and the cosmological term, Lambda, can be functions of a scale parameter mu. It turns out that G(mu) evolves according to a logarithmic law which may lead to asymptotic freedom of gravity, similar to the gauge coupling in QCD. At the same time Lambda(mu) evolves quadratically with mu. We study the consistency and cosmological consequences of these laws when \mu \simeq H . Furthermore, we propose to extend this method to the astrophysical domain after identifying the local RG scale at the galactic level. It turns out that Kepler's third law of celestial mechanics receives quantum corrections that may help to explain the flat rotation curves of the galaxies without introducing the dark matter hypothesis. The origin of these effects (cosmological and astrophysical) could be linked, in our framework, to physics at M_{\mathrm {X}}\sim 10^{16-17} GeV.
A time-dependent phenomenological model of , viz. is selected to investigate the -CDM cosmology. Time-dependent form of the equation of state parameter is derived and it has been possible to obtain the sought for flip of sign of the deceleration parameter q. Present age of the Universe, calculated for some specific values of the parameters agrees very well with the observational data.
We present photometric observations of an apparent Type Ia supernova (SN Ia) at a redshift of ~1.7, the farthest SN observed to date. The supernova, SN 1997ff, was discovered in a repeat observation by the Hubble Space Telescope (HST) of the Hubble Deep Field-North (HDF-N) and serendipitously monitored with NICMOS on HST throughout the Thompson et al. Guaranteed-Time Observer (GTO) campaign. The SN type can be determined from the host galaxy type: an evolved, red elliptical lacking enough recent star formation to provide a significant population of core-collapse supernovae. The classification is further supported by diagnostics available from the observed colors and temporal behavior of the SN, both of which match a typical SN Ia. The photometric record of the SN includes a dozen flux measurements in the I, J, and H bands spanning 35 days in the observed frame. The redshift derived from the SN photometry, z = 1.7 ± 0.1, is in excellent agreement with the redshift estimate of z = 1.65 ± 0.15 derived from the U300B450V606I814J110J125H160H165Ks photometry of the galaxy. Optical and near-infrared spectra of the host provide a very tentative spectroscopic redshift of 1.755. Fits to observations of the SN provide constraints for the redshift-distance relation of SNe Ia and a powerful test of the current accelerating universe hypothesis. The apparent SN brightness is consistent with that expected in the decelerating phase of the preferred cosmological model, ΩM ≈ 1/3,ΩΛ ≈ . It is inconsistent with gray dust or simple luminosity evolution, candidate astrophysical effects that could mimic previous evidence for an accelerating universe from SNe Ia at z ≈ 0.5. We consider several sources of potential systematic error, including gravitational lensing, supernova misclassification, sample selection bias, and luminosity calibration errors. Currently, none of these effects alone appears likely to challenge our conclusions. Additional SNe Ia at z > 1 will be required to test more exotic alternatives to the accelerating universe hypothesis and to probe the nature of dark energy.
We report measurements of the mass density, ΩM, and cosmological-constant energy density, ΩΛ, of the universe based on the analysis of 42 type Ia supernovae discovered by the Supernova Cosmology Project. The magnitude-redshift data for these supernovae, at redshifts between 0.18 and 0.83, are fitted jointly with a set of supernovae from the Calán/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All supernova peak magnitudes are standardized using a SN Ia light-curve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8ΩM-0.6ΩΛ≈-0.2±0.1 in the region of interest (ΩM1.5). For a flat (ΩM+ΩΛ=1) cosmology we find ΩMflat=0.28+0.09-0.08 (1 σ statistical) +0.05-0.04 (identified systematics). The data are strongly inconsistent with a Λ=0 flat cosmology, the simplest inflationary universe model. An open, Λ=0 cosmology also does not fit the data well: the data indicate that the cosmological constant is nonzero and positive, with a confidence of P(Λ>0)=99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t0flat=14.9+1.4-1.1(0.63/h) Gyr for a flat cosmology. The size of our sample allows us to perform a variety of statistical tests to check for possible systematic errors and biases. We find no significant differences in either the host reddening distribution or Malmquist bias between the low-redshift Calán/Tololo sample and our high-redshift sample. Excluding those few supernovae that are outliers in color excess or fit residual does not significantly change the results. The conclusions are also robust whether or not a width-luminosity relation is used to standardize the supernova peak magnitudes. We discuss and constrain, where possible, hypothetical alternatives to a cosmological constant.
We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 ≤ z ≤ 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmological parameters: the Hubble constant (H0), the mass density (ΩM), the cosmological constant (i.e., the vacuum energy density, ΩΛ), the deceleration parameter (q0), and the dynamical age of the universe (t0). The distances of the high-redshift SNe Ia are, on average, 10%–15% farther than expected in a low mass density (ΩM = 0.2) universe without a cosmological constant. Different light curve fitting methods, SN Ia subsamples, and prior constraints unanimously favor eternally expanding models with positive cosmological constant (i.e., ΩΛ > 0) and a current acceleration of the expansion (i.e., q0 < 0). With no prior constraint on mass density other than ΩM ≥ 0, the spectroscopically confirmed SNe Ia are statistically consistent with q0 < 0 at the 2.8 σ and 3.9 σ confidence levels, and with ΩΛ > 0 at the 3.0 σ and 4.0 σ confidence levels, for two different fitting methods, respectively. Fixing a "minimal" mass density, ΩM = 0.2, results in the weakest detection, ΩΛ > 0 at the 3.0 σ confidence level from one of the two methods. For a flat universe prior (ΩM + ΩΛ = 1), the spectroscopically confirmed SNe Ia require ΩΛ > 0 at 7 σ and 9 σ formal statistical significance for the two different fitting methods. A universe closed by ordinary matter (i.e., ΩM = 1) is formally ruled out at the 7 σ to 8 σ confidence level for the two different fitting methods. We estimate the dynamical age of the universe to be 14.2 ± 1.7 Gyr including systematic uncertainties in the current Cepheid distance scale. We estimate the likely effect of several sources of systematic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these effects appear to reconcile the data with ΩΛ = 0 and q0 ≥ 0.
We report measurements of ΩM, ΩΛ, and w from 11 supernovae (SNe) at z = 0.36-0.86 with high-quality light curves measured using WFPC2 on the Hubble Space Telescope (HST). This is an independent set of high-redshift SNe that confirms previous SN evidence for an accelerating universe. The high-quality light curves available from photometry on WFPC2 make it possible for these 11 SNe alone to provide measurements of the cosmological parameters comparable in statistical weight to the previous results. Combined with earlier Supernova Cosmology Project data, the new SNe yield a measurement of the mass density ΩM = 0.25 (statistical) ± 0.04 (identified systematics), or equivalently, a cosmological constant of ΩΛ = 0.75 (statistical) ± 0.04 (identified systematics), under the assumptions of a flat universe and that the dark energy equation-of-state parameter has a constant value w = -1. When the SN results are combined with independent flat-universe measurements of ΩM from cosmic microwave background and galaxy redshift distortion data, they provide a measurement of w = -1.05 (statistical) ± 0.09 (identified systematic), if w is assumed to be constant in time. In addition to high-precision light-curve measurements, the new data offer greatly improved color measurements of the high-redshift SNe and hence improved host galaxy extinction estimates. These extinction measurements show no anomalous negative E(B-V) at high redshift. The precision of the measurements is such that it is possible to perform a host galaxy extinction correction directly for individual SNe without any assumptions or priors on the parent E(B-V) distribution. Our cosmological fits using full extinction corrections confirm that dark energy is required with P(ΩΛ > 0) > 0.99, a result consistent with previous and current SN analyses that rely on the identification of a low-extinction subset or prior assumptions concerning the intrinsic extinction distribution.
We measure the large-scale real-space power spectrum PðkÞ by using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z % 0:1. We employ a matrix-based method using pseudo–Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 22 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0:02 h Mpc À1 < k < 0:3 h Mpc À1 . We pay par-ticular attention to modeling, quantifying, and correcting for potential systematic errors, nonlinear redshift distortions, and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum PðkÞ up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0:1 h Mpc À1 , thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the Wilkinson Microwave Anisotropy Probe satellite. The power spectrum is not well-characterized by a single power law but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fitted by a flat scale-invariant adiabatic cosmological model with h m ¼ 0:213 AE 0:023 and 8 ¼ 0:89 AE 0:02 for L Ã galaxies, when fixing the baryon fraction b = m ¼ 0:17 and the Hubble parameter h ¼ 0:72; cosmological interpretation is given in a companion paper.
The symmetric vacuum state in gauge theories with spontaneous symmetry breaking is symmetric in both internal and space-time
variables. We consider this vacuum state as a Bose condensate of physical Higgs particles, defined over an asymmetric vacuum
state, and identify the energy density of their self-interaction with the cosmological constant in the Einstein equation. In this picture, spontaneous symmetry breaking proceeds as decay. Decoherence of coherent oscillations of a scalar field in the course of decay provides the effective mechanism for damping of coherent oscillations, leading to the regime of slow evaporation of
a Bose condensate. This mechanism is responsible for self-consistent inflation without fine-tuning of the potential parameters.
The physical self-consistency in this model is provided by incorporating the origin of the cosmological constant in the dynamics
of spontaneous breaking of particle symmetries.
We consider the process of decay of symmetric vacuum state as evaporation of a Bose condensate of physical Higgs particles, defined over asymmetric vacuum state. Energy density of their selfinteraction is identified with cosmological constant in the Einstein equation. decay then provides dynamical realization of spontaneous symmetry breaking. The effective mechanism is found for damping of coherent oscillations of a scalar field, leading to slow evaporation regime as the effective mechanism for decay responsible for inflation without special fine-tuning of the microphysical parameters. This mechanism is able to incorporate reheating, generation of proper primordial fluctuations, and nonzero cosmological constant today.
Keeping in mind the current picture of an accelerating and flat Universe, some specific dynamical models of the cosmological term have been selected for investigating the nature of dark energy. Connecting the free parameters of the models with the cosmic matter and vacuum energy density parameters, it is shown that the models are equivalent. Using the selected models, the present values of some of the physical parameters have been estimated, and a glimpse at the past decelerating universe has also been presented. It is observed that most of these cosmological parameters nicely agree with the values suggested by the Type Ia Supernovae and other experimental data.
Two phenomenological models of , viz. and are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time as suggested earlier by others including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model is, in general, attractive in nature. Moreover, it is seen that due to the combined effect of time-variable and G the Universe evolved with acceleration as well as deceleration. This later one indicates a Big Crunch.
The production of Primordial Black Holes (PBH) from inflationary
perturbations provides a physical process where the effective
classicality of the fluctuations does not hold for certain scales. For
adiabatic perturbations produced during inflation, this range of scales
corresponds to PBH with masses M<<1015 g. For PBH with
masses M ~ MH(te), the horizon mass at the end of
inflation, the generation process during the preheating stage could be
classical as well, in contrast to the formation of PBH on these scales
by adiabatic inflationary perturbations. For the nonevaporated PBH, the
generation process is essentially classical.
The treatment of first-order phase transitions for standard grand unified theories is shown to break down for models with radiatively induced spontaneous symmetry breaking. It is argued that proper analysis of these transitions which would take place in the early history of the universe can lead to an explanation of the cosmological homogeneity, flatness, and monopole puzzles.
We study positive frequency mode solutions of a massive scalar field at an initial stage in the spatially flat, linearly expanding Robertson-Walker universe. The essential point is that the initial time is taken to be small enough, but nonzero (e.g., the Planck time), and the mode is determined by a kind of WKB condition. We calculate the created particle spectrum, and show that its low-energy behavior is considerably different from the previous results.
It is demonstrated that three reasonable physical criteria yield a unique Feynman propagator in a linearly expanding Robertson-Walker universe.
The standard model of hot big-bang cosmology requires initial conditions which are problematic in two ways: (1) The early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementary-particle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought.
Most models of dark energy predict the beginning of the accelerated epoch at z≤ 1. However, there is no observational or theoretical evidence in favour of such a recent start of the cosmic acceleration.
In fact, a model of dark energy coupled to dark matter is explicitly constructed which (a) is accelerated even at high z, (b) allows structure formation during acceleration, and (c) is consistent with the Type Ia supernovae Hubble diagram, including
the farthest known supernova SN1997ff at z≈ 1.7. It is shown that the accelerated epoch in this model could have started as early as z≈ 5.
High resolution, numerical simulations of 17 cluster-sized dark-matter haloes in eight different cosmologies with and without dynamical dark-energy confirm the picture that core halo densities are imprinted early during their formation by the mean cosmological density. Quite independent of cosmology, halo concentrations have a log-normal distribution with a scatter of &SIM; 0.2 about the mean. We propose a simple scaling relation for halo concentrations in dark-energy cosmologies. (C) 2005 Published by Elsevier B.V.
A new inflationary universe scenario is suggested, which is free of the shortcomings of the previous one and provides a possible solution of the horizon, flatness, homogeneity and isotropy problems in cosmology, and also a solution of the primordial monopole problem in grand unified theories.
Exploring the recent expansion history of the universe promises insights into the cosmological model, the nature of dark energy, and potentially clues to high energy physics theories and gravitation. We examine the extent to which precision distance-redshift observations can map out the history, including the acceleration-deceleration transition, and the components and equations of state of the energy density. We consider the ability to distinguish between various dynamical scalar field models for the dark energy, as well as higher dimension and alternate gravity theories. Finally, we present a new, advantageous parametrization for the study of dark energy.
We study the potential impact of improved future supernovae data on our understanding of the dark energy problem. We carefully examine the relative utility of different fitting functions that can be used to parameterize the dark energy models, and provide concrete reasons why a particular choice (based on a parameterization of the equation of state) is better in almost all cases. We discuss the details of a representative sample of dark energy models and show how future supernova observations could distinguish among these. As a specific example, we consider the proposed ``SNAP'' satellite which is planned to observe around 2000 supernovae. We show how a SNAP-class data set taken alone would be a powerful discriminator among a family of models that would be approximated by a constant equation of state for the most recent epoch of cosmic expansion. We show how this family includes most of the dark energy models proposed so far. We then show how an independent measurement of can allow SNAP to probe the evolution of the equation of state as well, allowing further discrimination among a larger class of proposed dark energy models. We study the impact of the satellite design parameters on this method to distinguish the models and compare SNAP to alternative measurements. We establish that if we exploit the full precision of SNAP it provides a very powerful probe. Comment: 29 pages, 22 figures; replaced to match version accepted for publication in PRD, section V shortend and merged into section VI; brief discussion on non-flat cosmologies added
We advance the viewpoint that only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute into the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. is of the order of the critical density. Thus the cosmological constant had to be smaller than the matter density in the past and will be bigger in the future. Comment: the version to appear in Mod.Phys.Lett. A
The presence of dark energy in the Universe is inferred directly from the
accelerated expansion of the Universe, and indirectly, from measurements of
cosmic microwave background (CMB) anisotropy. Dark energy contributes about 2/3
of the critical density, is very smoothly distributed, and has large negative
pressure. Its nature is very much unknown. Most of its discernible consequences
follow from its effect on evolution of the expansion rate of the Universe,
which in turn affects the growth of density perturbations and the age of the
Universe, and can be probed by the classical kinematic cosmological tests.
Absent a compelling theoretical model (or even a class of models), we describe
the dark energy by an effective equation-of-state w=p_X/\rho_X which is allowed
to vary with time. We describe and compare different approaches for determining
w(t), including magnitude-redshift (Hubble) diagram, number counts of galaxies
and clusters, and CMB anisotropy, focusing particular attention on the use of a
sample of several thousand type Ia supernova with redshifts z\lesssim 1.7, as
might be gathered by the proposed SNAP satellite. Among other things, we derive
optimal strategies for constraining cosmological parameters using type Ia
supernovae. While in the near term CMB anisotropy will provide the first
measurements of w, supernovae and number counts appear to have the most
potential to probe dark energy.
Friedmann-Robertson-Walker universes with a presently large fraction of the
energy density stored in an X-component with , are considered. We
find all the critical points of the system for constant equations of state in
that range. We consider further several background quantities that can
distinguish the models with different values. Using a simple toy model
with a varying equation of state, we show that even a large variation of
at small redshifts is very difficult to observe with measurements up
to . Therefore, it will require accurate measurements in the range
and independent accurate knowledge of (and/or
) in order to resolve a variable from a constant .
Current cosmological observations show a strong signature of the existence of a dark energy component with negative pressure. The most obvious candidate for this dark energy is the cosmological constant (with the equation of state w_X=p/\rho=-1), which, however, raises several theoretical difficulties. This has led to models for dark energy component which evolves with time. We discuss certain questions related to the determination of the nature of dark energy component from observations of high redshift supernova. The main results of our analysis are: (i) Even if the precise value of w_X is known from observations, it is not possible to determine the nature of the unknown dark energy source using only kinematical and geometrical measurements. We have given explicit examples to show that different types of sources can give rise to a given w_X. (ii) Although the full data set of supernova observations (which are currently available) strongly rule out models without dark energy, the high (z>0.25) and low (z<0.25) redshift data sets, individually, admit decelerating models with zero dark energy. Any possible evolution in the absolute magnitude of the supernovae, if detected, might allow the decelerating models to be consistent with the data. (iii) We have introduced two parameters, which can be obtained entirely from theory, to study the sensitivity of the luminosity distance on w_X. Using these two parameters, we have argued that although one can determine the present value of w_X accurately from the data, one cannot constrain the evolution of w_X.
Physics invites the idea that space contains energy whose gravitational effect approximates that of Einstein's cosmological constant, Lambda; nowadays the concept is termed dark energy or quintessence. Physics also suggests the dark energy could be dynamical, allowing the arguably appealing picture that the dark energy density is evolving to its natural value, zero, and is small now because the expanding universe is old. This alleviates the classical problem of the curious energy scale of order a millielectronvolt associated with a constant Lambda. Dark energy may have been detected by recent advances in the cosmological tests. The tests establish a good scientific case for the context, in the relativistic Friedmann-Lemaitre model, including the gravitational inverse square law applied to the scales of cosmology. We have well-checked evidence that the mean mass density is not much more than one quarter of the critical Einstein-de Sitter value. The case for detection of dark energy is serious but not yet as convincing; we await more checks that may come out of work in progress. Planned observations might be capable of detecting evolution of the dark energy density; a positive result would be a considerable stimulus to attempts to understand the microphysics of dark energy. This review presents the basic physics and astronomy of the subject, reviews the history of ideas, assesses the state of the observational evidence, and comments on recent developments in the search for a fundamental theory.
The dark energy that appears to produce the accelerating expansion of the universe can be characterized by an equation of state p=w\rho with w<-1/3. A number of observational tests have been proposed to study the value or redshift dependence of w, including SN Ia distances, the Sunyaev-Zel'dovich effect, cluster abundances, strong and weak gravitational lensing, galaxy and quasar clustering, galaxy ages, the \lya forest, and CMB anisotropies. The proposed observational tests based on these phenomena measure either the distance-redshift relation d(z), the Hubble parameter H(z), the age of the universe t(z), the linear growth factor D_1(z), or some combination of these quantities. We compute the evolution of these four observables, and of the combination H(z)d(z) that enters the Alcock-Paczyznski anisotropy test, in models with constant w, in quintessence models with some simple forms of the potential V(\phi), and in toy models that allow more radical time variations of w. Measurement of any of these quantities to precision of a few percent is generally sufficient to discriminate between w=-1 and w=-2/3. However, the time-dependence predicted in quintessence models is extremely difficult to discern because the quintessence component is dynamically unimportant at the redshifts where w departs substantially from its low-z value. Even for the toy models that allow substantial changes in w at low redshift, there is always a constant-w model that produces very similar evolution of all of the observables simultaneously. We conclude that measurement of the effective equation of state of the dark energy may be achieved by several independent routes in the next few years, but that detecting time-variation in this equation of state will prove very difficult except in specialized cases. Comment: 29 pages, 7 figures, many minor corrections, additions, and clarifications, to appear in ApJ
The formula for dark energy density derived by Gurzadyan and Xue provides a value of density parameter of dark energy in remarkable agreement with current cosmological datasets, unlike numerous phenomenological dark energy scenarios where the corresponding value is postulated. This formula suggests the possibility of variation of physical constants such as the speed of light and the gravitational constant. Considering several cosmological models based on that formula and deriving the cosmological equations for each case, we show that, in all models source terms appear in the continuity equation. So, one one hand, GX models make up a rich set covering a lot of currently proposed models of dark energy, on the other hand, they reveal hidden symmetries, with a particular role of the separatrix , and link with the issue of the content of physical constants.
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