Cosmographic transition redshift in $ f (R) $ gravity

Monthly Notices of the Royal Astronomical Society, 2012

The explanation of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. If the acceleration is driven by some form of dark energy, and in the absence of a well-based theory to interpret the observations, one can try to constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires only a minimal set of assumptions, namely to specify the metric, and it does not rely on the dynamical equations for gravity. Our high-redshift analysis allows us to put constraints on the cosmographic expansion up to the fifth order. It is based on the Union2 Type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some Gamma Ray Bursts luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC). We finally investigate implications of our results for the dark energy, in particular, we focus on the parametrization of the dark energy equation of state (EOS). Actually, a possibility to investigate the nature of dark energy lies in measuring the dark energy equation of state, w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of dark energy, described through several parametrizations of the equation of state, by comparing the cosmographic and the EOS series. 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 provides stronger constraints for parameter estimation, in particular for higher order cosmographic parameters (the jerk and the snap), with respect to those presented in the literature; d) both the estimation of the jerk and the DE parameters, reflect the possibility of a deviation from the ΛCDM cosmological model; e) there are indications that the dark energy equation of state is evolving for all the parametrizations that we considered; f ) the q(z) reconstruction provided by our cosmographic analysis allows a transient acceleration.

2020

In this work, we look at the cosmological constraints of some f(R)-modified gravity models such as f(R) = βR (a toy model) and more realistic ones like the Starobinsky and Hu-Sawicki models. We use 236 intermediate-redshift and 123 low-redshift Type 1A Supernovae data obtained from the SDSS-II/SNLS3 Joint Light-curve Analysis (JLA), with absolute magnitudes, for the B-filter, found on the NASA Extragalactic Database (NED). We then develop a Markov Chain Monte-Carlo (MCMC) simulation to find the best fit (firstly to the ΛCDM model), to obtain the cosmological parameters (Ωm and h̄). We then use the concordance model results to constrain the priors for the f(R)-gravity models on the MCMC simulation. We assume a flat universe Ωk = 0 and a radiation density Ωr that is negligible in both the ΛCDM model and f(R)-gravity models. Thus, the only difference between the ΛCDM model and f(R)-gravity models will be dark energy and the arbitrary free parameters. This will tell us if there exist vi...

2012

The explanation of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. If the acceleration is driven by some form of dark energy, one can try to constrain the parameters using a cosmographic approach. Our high-redshift analysis allows us to put constraints on the cosmographic expansion up to the fifth order. It is based on the Union2 Type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some Gamma Ray Bursts luminosity distance indicators, and gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC). We finally investigate implications of our results for the dark energy, in particular, we focus on the parametrization of the dark energy equation of state (EOS). Actually, a possibility to investigate the nature of dark energy lies in measuring the dark energy equation of state, w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of dark energy, described through several parametrizations of the equation of state, by comparing the cosmographic and the EOS series.

Monthly Notices of the Royal Astronomical Society, 2017

The standard relation between the cosmological redshift and cosmic scalefactor underlies cosmological inference from virtually all kinds of cosmological observations, leading to the emergence of the cold-dark-matter ( CDM) cosmological model. This relation is not a fundamental theory and thus observational determination of this function (redshift remapping) should be regarded as an insightful alternative to holding its standard form in analyses of cosmological data. Here we present non-parametric reconstructions of redshift remapping in dark-matter-dominated models and constraints on cosmological parameters from a joint analysis of all primary cosmological probes including the local measurement of the Hubble constant, Type Ia supernovae, baryon acoustic oscillations (BAO), Planck observations of the cosmic microwave background (CMB) radiation (temperature power spectrum) and cosmic chronometers. The reconstructed redshift remapping points to an additional boost of redshift operating in late epoch of cosmic evolution, but affecting both low-redshift observations and the CMB. The model predicts a significant difference between the actual Hubble constant, h = 0.48 ± 0.02, and its local determination, h obs = 0.73 ± 0.02. The ratio of these two values coincides closely with the maximum expansion rate inside voids formed in the corresponding open cosmological model with m = 0.87 ± 0.03, whereas the actual value of the Hubble constant implies the age of the Universe that is compatible with the Planck CDM cosmology. The model with redshift remapping provides excellent fits to all data and eliminates recently reported tensions between the Planck CDM cosmology, the local determination of the Hubble constant and the BAO measurements from the Ly α forest of high-redshift quasars.

The Astrophysical Journal Letters, 2006

Modified f (R) gravity in the Palatini approach has been presently applied to Cosmology as a realistic alternative to dark energy. In this concern, a number of authors have searched for observational constraints on several f (R) gravity functional forms using mainly data of type Ia supenovae (SNe Ia), Cosmic Microwave Background (CMB) radiation and Large Scale Structure (LSS). In this paper, by considering a homogeneous and isotropic flat universe, we use determinations of the Hubble function H(z), which are based on differential age method, to place bounds on the free parameters of the f (R) = R − β/R n functional form. We also combine the H(z) data with constraints from Baryon Acoustic Oscillations (BAO) and CMB measurements, obtaining ranges of values for n and β in agreement with other independent analyses. We find that, for some intervals of n and β, models based on f (R) = R − β/R n gravity in the Palatini approach, unlike the metric formalism, can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy.

to appear in MNRAS

The understanding of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. Whether or not the acceleration is driven by some form of dark energy, and in the absence of a well-based theory to interpret the observations, many models have been proposed to solve this problem, both in the context of General Relativity and alternative theories of gravity. Actually, a further possibility to investigate the nature of dark energy lies in measuring the dark energy equation of state (EOS), w, and its time (or redshift) dependence at high accuracy. However, since w(z) is not directly accessible to measurement, reconstruction methods are needed to extract it reliably from observations. Here we investigate different models of dark energy, described through several parametrizations of the EOS. Our high-redshift analysis is based on the Union2 Type Ia Supernovae (SNIa) data set, the Hubble diagram constructed from some Gamma Ray Bursts (GRBs) luminosity distance indicators, and Gaussian priors on the distance from the Baryon Acoustic Oscillations (BAO), and the Hubble constant h (these priors have been included in order to help break the degeneracies among model parameters). To perform our statistical analysis and to explore the probability distributions of the EOS parameters we use the Markov Chain Monte Carlo Method (MCMC). It turns out that the dark energy equation of state is evolving for all the parametrizations that we considered. We finally compare our results with the ones obtained by previous cosmographic analysis performed on the same astronomical datasets, showing that the latter ones are sufficient to test and compare the new parametrizations.

Journal of Cosmology and Astroparticle Physics, 2010

We constrain the parameters describing the kinematical state of the universe using a cosmographic approach, which is fundamental in that it requires a very minimal set of assumptions (namely to specify a metric) and does not rely on the dynamical equations for gravity. On the data side, we consider the most recent compilations of Supernovae and Gamma Ray Bursts catalogues. This allows to further extend the cosmographic fit up to z = 6.6, i.e. up to redshift for which one could start to resolve the low z degeneracy among competing cosmological models. In order to reliably control the cosmographic approach at high redshifts, we adopt the expansion in the improved parameter y = z/(1 + z). This series has the great advantage to hold also for z > 1 and hence it is the appropriate tool for handling data including non-nearby distance indicators. We find that Gamma Ray Bursts, probing higher redshifts than Supernovae, have constraining power and do require (and statistically allow) a cosmographic expansion at higher order than Supernovae alone. Exploiting the set of data from Union and GRBs catalogues, we show (for the first time in a purely cosmographic approach parametrized by deceleration q 0 , jerk j 0 , snap s 0) a definitively negative deceleration parameter q 0 up to the 3σ confidence level. We present also forecasts for realistic data sets that are likely to be obtained in the next few years.

In this paper, we use the cosmokinematics approach to study the accelerated expansion of the Universe. This is a model independent approach and depends only on the assumption that the Universe is homogeneous and isotropic and is described by the FRW metric. We parametrize the deceleration parameter, q(z), to constrain the transition redshift (z t) at which the expansion of the Universe goes from a decelerating to an accelerating phase. We use three different parametrizations of q(z) namely, q I (z) = q 1 + q 2 z, q II (z) = q 3 + q 4 ln(1 + z) and q III (z) = 1 2 + q 5 (1+z) 2. A joint analysis of the age of galaxies, strong lensing and supernovae Ia data indicates that the transition redshift is less than unity i.e. z t < 1. We also use a nonparametric approach (LOESS+SIMEX) to constrain z t. This too gives z t < 1 which is consistent with the value obtained by the parametric approach.

Journal of Cosmology and Astroparticle Physics, 2015

In this paper, we use the cosmokinematics approach to study the accelerated expansion of the Universe. This is a model independent approach and depends only on the assumption that the Universe is homogeneous and isotropic and is described by the FRW metric. We parametrize the deceleration parameter, q(z), to constrain the transition redshift (z t) at which the expansion of the Universe goes from a decelerating to an accelerating phase. We use three different parametrizations of q(z) namely, q I (z) = q 1 + q 2 z, q II (z) = q 3 + q 4 ln(1 + z) and q III (z) = 1 2 + q 5 (1+z) 2. A joint analysis of the age of galaxies, strong lensing and supernovae Ia data indicates that the transition redshift is less than unity i.e. z t < 1. We also use a nonparametric approach (LOESS+SIMEX) to constrain z t. This too gives z t < 1 which is consistent with the value obtained by the parametric approach.

Physical Review D, 2008

Using techniques from singular perturbation theory, we explicitly calculate the cosmological evolution in a class of modified gravity models. By considering the (m)CDTT model, which aims to explain the current acceleration of the universe with a modification of gravity, we show that Einstein evolution can be recovered for most of cosmic history in at least one f (R) model. We show that a standard epoch of matter domination can be obtained in the mCDTT model, providing a sufficiently long epoch to satisfy observations. We note that the additional inverse term will not significantly alter standard evolution until today and that the solution lies well within present constraints from Big Bang Nucleosynthesis. For the CDTT model, we analyse the "recent radiation epoch" behaviour (a ∝ t 1/2 ) found by previous authors. We finally generalise our findings to the class of inverse power-law models. Even in this class of models, we expect a standard cosmological evolution, with a sufficient matter domination era, although the sign of the additional term is crucial.