Content uploaded by Salvatore Capozziello

Author content

All content in this area was uploaded by Salvatore Capozziello

Content may be subject to copyright.

A preview of the PDF is not available

We study the possibility to extract model independent information about the
dynamics of the universe by using Cosmography. We intend to explore it
systematically, to learn about its limitations and its real possibilities. Here
we are sticking to the series expansion approach on which Cosmography is based.
We apply it to different data sets: Supernovae Type Ia (SNeIa), Hubble
parameter extracted from differential galaxy ages, Gamma Ray Bursts (GRBs) and
the Baryon Acoustic Oscillations (BAO) data. We go beyond past results in the
literature extending the series expansion up to the fourth order in the scale
factor, which implies the analysis of the deceleration, q_{0}, the jerk, j_{0}
and the snap, s_{0}. We use the Markov Chain Monte Carlo Method (MCMC) to
analyze the data statistically. We also try to relate direct results from
Cosmography to dark energy (DE) dynamical models parameterized by the
Chevalier-Polarski-Linder (CPL) model, extracting clues about the matter
content and the dark energy parameters. The main results are: a) even if
relying on a mathematical approximate assumption such as the scale factor
series expansion in terms of time, cosmography can be extremely useful in
assessing dynamical properties of the Universe; b) the deceleration parameter
clearly confirms the present acceleration phase; c) the MCMC method can help
giving narrower constraints in parameter estimation, in particular for higher
order cosmographic parameters (the jerk and the snap), with respect to the
literature; d) both the estimation of the jerk and the DE parameters, reflect
the possibility of a deviation from the LCDM cosmological model.

Figures - uploaded by Salvatore Capozziello

Author content

All figure content in this area was uploaded by Salvatore Capozziello

Content may be subject to copyright.

Content uploaded by Salvatore Capozziello

Author content

All content in this area was uploaded by Salvatore Capozziello

Content may be subject to copyright.

A preview of the PDF is not available

... where the cosmographical parameters (Capozziello et al. 2011): Hubble parameter H, deceleration parameter q, jerk parameter j, snap parameter s, and lerk parameter l are defined as ...

Taking advantage of Gaussian process (GP), we obtain an improved estimate of the Hubble constant, $H_0=70.41\pm1.58$ km s$^{-1}$ Mpc$^{-1}$, using Hubble parameter [$H(z)$] from cosmic chronometers (CCH) and expansion rate function [$E(z)$], extracted from type Ia supernovae, data. This result is higher than those obtained by directly reconstructing CCH data with GP. In order to estimate the potential of future CCH data, we simulate two sets of $H(z)$ data and use them to constrain $H_0$ by either using GP reconstruction or fitting them with $E(z)$ data. We find that simulated $H(z)$ data alleviate $H_0$ tension by pushing $H_0$ values higher towards $\sim70$ km s$^{-1}$ Mpc$^{-1}$. We also find that joint $H(z)$ + $E(z)$ data favor higher values of $H_0$, which is also confirmed by constraining $H_0$ in the flat concordance model and 2-order Taylor expansion of $H(z)$. In summary, we conclude that more and better-quality CCH data as well as $E(z)$ data can provide a new and useful perspective on resolving $H_0$ tension.

... Interestingly, some cosmographic analyses lead to deviations from the concordance model, see e.g. [51] and [52,53]. In these works, it is shown that on pure cosmographic grounds the confidence level at which we may claim that the Universe is currently accelerating is moderate, if we rely on the data on SnIa+CCH only, whereas it is very strong when BAOs are also included. ...

We perform a comparative study of different types of dynamical dark energy models (DDES) using the cosmographic method. Among the models being examined herein we have the Running Vacuum models (RVMs), which have demonstrated considerable ability to fit the overall cosmological data at a level comparable to the standard cosmological model, $\Lambda$CDM, and capable of alleviating the $\sigma_8$ and $H_0$ tensions. At the same time we address a variety of Holographic dark energy models (HDEs) with different options for the time (redshift)-varying model parameter $c=c(z)$. We deal with the HDEs under the double assumption of fixed and evolving holographic length scale and assess which one is better. Both types of DDEs (RVMs and HDEs) are confronted with the most robust cosmographic data available, namely the Pantheon sample of supernovae (SnIa), the baryonic acoustic oscillation data (BAOs) extracted from measurement of the power spectrum and bispectrum of the BOSS data release, and the cosmic chronometer measurements of the Hubble rate (CCHs) at different redshifts obtained from spectroscopic observations of passively evolving galaxies. Using these data samples we assess the viability of the mentioned DDEs and compare them with the concordance $\Lambda$CDM model. From cosmographic analysis we conclude that the RVMs fare comparably well to the $\Lambda$CDM, a fact which adds up more credit to their sound phenomenological status. In contrast, while some of the HDEs are favored using the current Hubble horizon as fixed holographic length, they become highly unfavoured in the more realistic case when the holographic length is dynamical and evolves as the Hubble horizon.

... The z-redshift method is the earliest Taylor series used in cosmology. The luminosity distance can be conveniently expressed as (Cattoën & Visser 2007;Capozziello et al. 2011), where H 0 , q 0 , j 0 , s 0 , and l 0 are the current values. The first two terms above are Weinberg's version of the Hubble law which can be found from equation (14.6.8) in the book by Weinberg (1972). ...

Cosmography is used in cosmological data processing in order to constrain the kinematics of the universe in a model-independent way. In this paper, we first investigate the effect of the ultraviolet (UV) and X-ray relation of a quasar on cosmological constraints. By fitting the quasar relation and cosmographic parameters simultaneously, we find that the 4$\sigma$ deviation from the cosmological constant cold dark matter ($\Lambda$CDM) model disappears. Next, utilizing the Pantheon sample and 31 long gamma-ray bursts (LGRBs), we make a comparison among the different cosmographic expansions ($z$-redshift, $y$-redshift, $E(y)$, $\log(1+z)$, $\log(1+z)+k_{ij}$, and Pad$\rm \acute{e}$ approximations) with the third-order and fourth-order expansions. The expansion order can significantly affect the results, especially for the $y$-redshift method. Through analysis from the same sample, the lower-order expansion is preferable, except the $y$-redshift and $E(y)$ methods. For the $y$-redshift and $E(y)$ methods, despite adopting the same parameterization of $y=z/(1+z)$, the performance of the latter is better than that of the former. Logarithmic polynomials, $\log(1+z)$ and $\log(1+z) + k_{ij}$, perform significantly better than $z$-redshift, $y$-redshift, and $E(y)$ methods, but worse than Pad$\rm \acute{e}$ approximations. Finally, we comprehensively analyze the results obtained from different samples. We find that the Pad$\rm \acute{e}_{(2,1)}$ method is suitable for both low and high redshift cases. The Pad$\rm \acute{e}_{(2,2)}$ method performs well in a high-redshift situation. For the $y$-redshift and $E(y)$ methods, the only constraint on the first two parameters ($q_{0}$ and $j_{0}$) is reliable.

In this paper, we study the power-law f(T) model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), Gamma Ray Bursts (GRBs) and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method. Using mock data for SNIa, QSOs and GRBs generated based on the power-law f(T) model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not. In particular, we investigate the rational PADE polynomials (3,2) and (2,2) in addition to the fourth- and fifth- order Taylor series. We show that PADE (3,2) is the best approximation that can be used in the cosmographic method to reconstruct the distance modulus at both low and high redshifts. In the context of PADE (3,2) cosmographic method, we show that the power-law f(T) model is well consistent with the real observational data from the Hubble diagrams of SNIa, QSOs and GRBs. Moreover, we find that the combination of the Hubble diagram of SNIa and the BAO observation leads to better consistency between the model-independent cosmographic method and the power-law f(T) model. Finally, our observational constraints on the parameter of the effective equation of state of DE, described by the power-law f(T) model, show the phantom-like behavior, especially when the BAO observations are included in our analysis.

In this paper, we investigate the homogeneous and isotropic flat FLRW Universe in the logarithmic form of f(Q) gravity, where Q is the non-metricity scalar, specifically, f(Q)=α+βlog(Q), where α and β are free model parameters. In this study, we consider a parametrization of the Hubble parameter as H(z)=η[(z+1)^{-γ}+1], where γ and η are model/free parameters which are constrained by an R²-test from 57 points of the Hubble datasets in the redshift range 0.07<z<2.36. Further, we investigate the physical properties of the model. We analyze the energy conditions to check the compatibility of the model. We found the SEC is violated for the logarithmic form of f(Q) gravity due to the reality that the Universe in an accelerating phase. Finally, we discuss some important cosmological parameters in this context to compare our model with dark energy models such as jerk parameter and statefinder parameters.

In this work, we study the cosmological implications of Kaniadakis holographic dark energy model in the context of Einstein and deformed Hořava-Lifshitz theories of gravity. We examine the various cosmological parameters to analyze the evolution of the universe. The Hubble parameter [Formula: see text] is discussed as it is evidence for accelerating universe and source to examine some other cosmological parameters. We probe coincidence parameter [Formula: see text] to check the matter- and energy-dominated eras of the universe. The deceleration parameter [Formula: see text] is explored for the expansion behavior of the universe while the jerk parameter [Formula: see text] is examined to compare the different dark energy models with [Formula: see text]CDM [Formula: see text] model. We examine the equation of state parameter [Formula: see text] to look into different phases of the universe. We calculate the perturbed parameter squared speed of sound [Formula: see text] to assess the stable behavior of the model. We also investigate the behavior of rate of change of entropy to discuss the validity of generalized second law of thermodynamics.

We propose a new parametrization of dark energy motivated by thermodynamics. To this aim, we consider Padé polynomials to reconstruct the form of deceleration parameter adequate to describe different epochs of cosmic history and divergence-free in the far future. The proposed scenario also fulfills the demand of structure formation and contains the ΛCDM model as a limiting case. Thus, a numerical analysis at both background and perturbation levels is performed through the Markov Chain Monte Carlo method in view of the most recent cosmic data. We then use the observational constraints to explore the features of dark energy evolution and compare our findings with the predictions of the standard cosmological model.

Gamma-ray bursts (GRBs) detected at high redshift can be used to trace the cosmic expansion history. However, the calibration of their luminosity distances is not an easy task in comparison to Type Ia Supernovae (SNeIa). To calibrate these data, correlations between their luminosity and other observed properties of GRBs need to be identified, and we must consider the validity of our assumptions about these correlations over their entire observed redshift range. In this work, we propose a new method to calibrate GRBs as cosmological distance indicators using SNeIa observations with a machine learning architecture. As well we include a new data GRB calibrated sample using extended cosmography in a redshift range above z > 3.6. An overview of this machine learning technique was developed in [1] to study the evolution of dark energy models at high redshift. The aim of the method developed in this work is to combine two networks: a Recurrent Neural Network (RNN) and a Bayesian Neural Network (BNN). Using this computational approach, denoted RNN+BNN, we extend the network's efficacy by adding the computation of covariance matrices to the Bayesian process. Once this is done, the SNeIa distance-redshift relation can be tested on the full GRB sample and therefore used to implement a cosmographic reconstruction of the distance-redshift relation in different regimes. Thus, our newly-trained neural network is used to constrain the parameters describing the kinematical state of the Universe via a cosmographic approach at high redshifts (up to z ≈ 10), wherein we require a very minimal set of assumptions on the deep learning arquitecture itself that do not rely on dynamical equations for any specific theory of gravity.

We propose a model-independent parametrization of dark energy motivated by thermodynamics. To this aim, we consider Pad\'e polynomials to reconstruct the form of deceleration parameter adequate to describe different epochs of cosmic history and divergence-free in the far future. The proposed scenario also fulfills the demand of structure formation and contains the $\Lambda$CDM model as a limiting case. Thus, a numerical analysis at both background and perturbation levels is performed through the Markov Chain Monte Carlo method in view of the most recent cosmic data. We then use the observational constraints to explore the features of dark energy evolution and compare our findings with the predictions of the standard cosmological model.

The Hubble tension, if not caused by any systematics, could be relieved or even resolved from modifying either the early-time or late-time Universe. The early-time modifications are usually in tension with either galaxy clustering or galaxy lensing constraints. The late-time modifications are also in conflict with the constraint from the inverse distance ladder, which, however, is weakened by the dependence on a sound-horizon prior and some particular approximation for the late-time expansion history. To achieve a more general no-go argument for the late-time scenarios, we propose to use a global parametrization based on the cosmic age to consistently use the cosmic chronometers data beyond the Taylor expansion domain and without the input of a sound-horizon prior. Both the early-time and late-time scenarios are therefore largely ruled out, indicating the possible ways out of the Hubble tension from either exotic modifications of our concordance Universe or some unaccounted for systematics.

We present multiband photometry of 185 type-Ia supernovae (SNe Ia), with over 11,500 observations. These were acquired between 2001 and 2008 at the F. L. Whipple Observatory of the Harvard-Smithsonian Center for Astrophysics (CfA). This sample contains the largest number of homogeneously observed and reduced nearby SNe Ia (z 0.08) published to date. It more than doubles the nearby sample, bringing SN Ia cosmology to the point where systematic uncertainties dominate. Our natural system photometry has a precision of 0.02 mag in BVRIr'i' and 0.04 mag in U for points brighter than 17.5 mag. We also estimate a systematic uncertainty of 0.03 mag in our SN Ia standard system BVRIr'i' photometry and 0.07 mag for U. Comparisons of our standard system photometry with published SN Ia light curves and comparison stars, where available for the same SN, reveal agreement at the level of a few hundredths mag in most cases. We find that 1991bg-like SNe Ia are sufficiently distinct from other SNe Ia in their color and light-curve-shape/luminosity relation that they should be treated separately in light-curve/distance fitter training samples. The CfA3 sample will contribute to the development of better light-curve/distance fitters, particularly in the few dozen cases where near-infrared photometry has been obtained and, together, can help disentangle host-galaxy reddening from intrinsic supernova color, reducing the systematic uncertainty in SN Ia distances due to dust.

It has recently been pointed out by Kowalski et. al. (arxiv:0804.4142) that
there is `an unexpected brightness of the SnIa data at z>1'. We quantify this
statement by constructing a new statistic which is applicable directly on the
Type Ia Supernova (SnIa) distance moduli. This statistic is designed to pick up
systematic brightness trends of SnIa datapoints with respect to a best fit
cosmological model at high redshifts. It is based on binning the normalized
differences between the SnIa distance moduli and the corresponding best fit
values in the context of a specific cosmological model (eg LCDM). We then focus
on the highest redshift bin and extend its size towards lower redshifts until
the Binned Normalized Difference (BND) changes sign (crosses 0) at a redshift
z_c (bin size N_c). The bin size N_c of this crossing (the statistical
variable) is then compared with the corresponding crossing bin size N_{mc} for
Monte Carlo data realizations based on the best fit model. We find that the
crossing bin size N_c obtained from the Union08 and Gold06 data with respect to
the best fit LCDM model is anomalously large compared to N_{mc} of the
corresponding Monte Carlo datasets obtained from the best fit LCDM in each
case. In particular, only 2.2% of the Monte Carlo LCDM datasets are consistent
with the Gold06 value of N_c while the corresponding probability for the
Union08 value of N_c is 5.3%. Thus, according to this statistic, the
probability that the high redshift brightness bias of the Union08 and Gold06
datasets is realized in the context of a (w_0,w_1)=(-1,0) model (LCDM
cosmology) is less than 6%. The corresponding realization probability in the
context of a (w_0,w_1)=(-1.4,2) model is more than 30% for both the Union08 and
the Gold06 datasets.

We perform a cosmographic analysis using several cosmological observables such as the luminosity distance moduli, the volume distance, the angular diameter distance and the Hubble parameter. These quantities are determined using different data sets: supernovae type Ia and gamma ray bursts, the baryonic acoustic oscillations, the cosmic microwave background power spectrum and the Hubble parameter as measured from surveys of galaxies. This data set allows us to put constraints on the cosmographic expansion with unprecedented precision. We also present forecasts for the coefficients of the kinematic expansion using future but realistic data sets: constraints on the coefficients of the expansions are likely to improve by a factor of 10 with the upcoming large scale structure probes. Finally, we derive the set of the cosmographic parameters for several cosmological models (including ΛCDM) and compare them with our best fit set. While distance measurements are unable to discriminate among these models, we show that the inclusion of the Hubble data set leads to strong constraints on the lowest order coefficients and, in particular, it is incompatible with ΛCDM at 3-σ confidence level. We discuss the reliability of this determination and suggest further observations which might be of crucial importance for the viability of cosmographic tests in the future.

We report on work to increase the number of well-measured Type Ia supernovae (SNe Ia) at high redshifts. Light curves, including high signal-to-noise Hubble Space Telescope data, and spectra of six SNe Ia that were discovered during 2001, are presented. Additionally, for the two SNe with z > 1, we present ground-based J-band photometry from Gemini and the Very Large Telescope. These are among the most distant SNe Ia for which ground-based near-IR observations have been obtained. We add these six SNe Ia together with other data sets that have recently become available in the literature to the Union compilation. We have made a number of refinements to the Union analysis chain, the most important ones being the refitting of all light curves with the SALT2 fitter and an improved handling of systematic errors. We call this new compilation, consisting of 557 SNe, the Union2 compilation. The flat concordance ΛCDM model remains an excellent fit to the Union2 data with the best-fit constant equation-of-state parameter w = –0.997+0.050 –0.054(stat)+0.077 –0.082(stat + sys together) for a flat universe, or w = –1.038+0.056 –0.059(stat)+0.093 –0.097(stat + sys together) with curvature. We also present improved constraints on w(z). While no significant change in w with redshift is detected, there is still considerable room for evolution in w. The strength of the constraints depends strongly on redshift. In particular, at z 1, the existence and nature of dark energy are only weakly constrained by the data.

We place constraints on the redshift-averaged, effective value of the equation of state of dark energy, w, using only the absolute ages of Galactic stars and the observed position of the first peak in the angular power spectrum of the cosmic microwave background (CMB). We find w < -0.8 at the 68% confidence level. If we further consider that w ≥ -1, this finding suggests that within our uncertainties, dark energy is indistinguishable from a classical vacuum energy term. We detect a correlation between the ages of the oldest galaxies and their redshift. This opens up the possibility of measuring w(z) by computing the relative ages of the oldest galaxies in the universe as a function of redshift, dz/dt. We show that this is a realistic possibility by computing dz/dt at z ~ 0 from Sloan Digital Sky Survey (SDSS) galaxies and obtain an independent estimate for the Hubble constant, H0 = 69 ± 12 km s-1 Mpc-1. The small number of galaxies considered at z > 0.2 does not yield, currently, a precise determination of w(z), but shows that the age-redshift relation is consistent with a standard ΛCDM universe with w = -1.

The apparent magnitude-redshift data of Type Ia supernovae (SNe Ia) call for modifications in the standard model energy densities. Under the circumstance that this modification cannot be limited to the addition of a mere cosmological constant, a serious situation has emerged in cosmology in which the energy densities in the universe have become largely speculative. In this situation, an equation of state of the form p = wρ itself is not well motivated. In this paper, we argue that 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 Robertson-Walker metric. This cosmographic approach is historically the original one in cosmology. We perform the analysis by expanding the scale factor into a fifth-order polynomial, an assumption that can be further generalized to any order. The present expansion rates h, q0, r0, etc., are evaluated by computing the marginal likelihoods for these parameters. These values are relevant since any cosmological solution would ultimately need to explain them.

We present a new compilation of Type Ia supernovae (SNe Ia), a new data set of low-redshift nearby-Hubble-flow SNe, and new analysis procedures to work with these heterogeneous compilations. This "Union" compilation of 414 SNe Ia, which reduces to 307 SNe after selection cuts, includes the recent large samples of SNe Ia from the Supernova Legacy Survey and ESSENCE Survey, the older data sets, as well as the recently extended data set of distant supernovae observed with the Hubble Space Telescope (HST). A single, consistent, and blind analysis procedure is used for all the various SN Ia subsamples, and a new procedure is implemented that consistently weights the heterogeneous data sets and rejects outliers. We present the latest results from this Union compilation and discuss the cosmological constraints from this new compilation and its combination with other cosmological measurements (CMB and BAO). The constraint we obtain from supernovae on the dark energy density is ΩΛ = 0.713+ 0.027−0.029(stat)+ 0.036−0.039(sys) , for a flat, ΛCDM universe. Assuming a constant equation of state parameter, w, the combined constraints from SNe, BAO, and CMB give w = − 0.969+ 0.059−0.063(stat)+ 0.063−0.066(sys) . While our results are consistent with a cosmological constant, we obtain only relatively weak constraints on a w that varies with redshift. In particular, the current SN data do not yet significantly constrain w at z > 1. With the addition of our new nearby Hubble-flow SNe Ia, these resulting cosmological constraints are currently the tightest available.

We present ugriz light curves for 146 spectroscopically-confirmed or spectroscopically-probable Type Ia supernovae (SNe) from the 2005 season of the Sloan Digital Sky Survey-II Supernova (SN) survey. The light curves have been constructed using a photometric technique that we call scene modeling, which is described in detail here; the major feature is that SN brightnesses are extracted from a stack of images without spatial resampling or convolution of the image data. This procedure produces accurate photometry along with accurate estimates of the statistical uncertainty, and can be used to derive photometry taken with multiple telescopes. We discuss various tests of this technique that demonstrate its capabilities. We also describe the methodology used for the calibration of the photometry, and present calibrated magnitudes and fluxes for all of the spectroscopic SNe Ia from the 2005 season.

Sampling, Statistics and Computer Code Error Analysis for Independent Random Variables Markov Chain Monte Carlo Error Analysis for Markov Chain Data Advanced Monte Carlo Parallel Computing Conclusions, History and Outlook.

This is the second of two papers reporting results from a program to determine the Hubble constant to ∼ 5 % precision from a refurbished distance ladder based on extensive use of differential measurements. Here we report observations of 240 Cepheid variables obtained with the Near Infrared Camera and Multi-Object Spectrometer (NIC-MOS) Camera 2 through the F160W filter on the Hubble Space Telescope (HST). The Cepheids are distributed across six recent hosts of Type Ia supernovae (SNe Ia) and the “maser galaxy ” NGC 4258, allowing us to directly calibrate the peak luminosities of the SNe Ia from the precise, geometric distance measurements provided by the masers. New features of our measurement include the use of the same instrument for all Cepheid measurements across the distance ladder and homogeneity of the Cepheid periods and metallicities thus necessitating only a differential measurement of Cepheid fluxes and reducing the largest systematic uncertainties in the determination of the fiducial SN Ia luminosity. In addition, the NICMOS measurements reduce the effects of differential extinction in the host galaxies by a factor of ∼5 over past optical data. Combined