Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the ΛCDM model, based on General Relativity and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of General Relativity are taken into account, with particular attention to f (R) and f (T ) theories of gravity where dynamics is represented by curvature or torsion field respectively. The features of f (R) models are explored in metric and Palatini formalisms. We discuss the connection between f (R) gravity and scalar-tensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of f (R) models is investigated through the corresponding viability criteria. Afterwards, the equivalent formulation of General Relativity (Teleparallel Equivalent General Relativity) in terms of torsion and its extension to f (T ) gravity is considered. Finally, the cosmographic method is adopted to break the degeneracy among dark energy models. A novel approach, built upon rational Padé and Chebyshev polynomials, is proposed to overcome limits of standard cosmography based on Taylor expansion. The approach provides accurate model-independent approximations of the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain integration of cosmic data, are presented to bound coefficients of the cosmographic series. These techniques are thus applied to reconstruct f (R) and f (T ) functions and to frame the late-time expansion history of the universe with no a priori assumptions on April 3, 2019 0:31 WSPC/INSTRUCTION FILE Review 2 S. Capozziello, R. D'Agostino, O. Luongo its equation of state. A comparison between the ΛCDM cosmological model with f (R) and f (T ) models is reported.

We here propose a new model-independent technique to overcome the circularity problem affecting the use of gamma-ray bursts (GRBs) as distance indicators through the use of Ep−Eiso correlation. We calibrate the Ep−Eiso correlation and find the GRB distance moduli that can be used to constrain dark energy models. We use observational Hubble data to approximate the cosmic evolution through Bézier parametric curve obtained through the linear combination of Bernstein basis polynomials. In doing so, we build up a new data set consisting of 193 GRB distance moduli. We combine this sample with the supernova JLA data set to test the standard ΛCDM model and its wCDM extension. We place observational constraints on the cosmological parameters through Markov Chain Monte Carlo numerical technique. Moreover, we compare the theoretical scenarios by performing the Akaike and Deviance Information statistical criteria.the 2σ level, while for the wCDM model we obtain $\Omega _m=0.34^{+0.13}_{-0.15}$ and $w=-0.86^{+0.36}_{-0.38}$ at the 2σ level. Our analysis suggests that ΛCDM model is statistically favoured over the wCDM scenario. No evidence for extension of the ΛCDM model is found.

Cosmography becomes non-predictive when cosmic data span beyond the red shift limit z ≃ 1. This leads to a strong convergence issue that jeopardizes its viability. In this work, we critically compare the two main solutions of the convergence problem, i.e. the y-parametrizations of the redshift and the alternatives to Taylor expansions based on Padé series. In particular, among several possibilities, we consider two widely adopted parametrizations, namely y 1 = 1 − a and y 2 = arctan(a −1 − 1), being a the scale factor of the Universe. We find that the y 2 -parametrization performs relatively better than the y 1 -parametrization over the whole redshift domain. Even though y 2 overcomes the issues of y 1 , we get that the most viable approximations of the luminosity distance d L (z) are given in terms of Padé approximations. In order to check this result by means of cosmic data, we analyze the Padé approximations up to the fifth order, and compare these series with the corresponding y-variables of the same orders. We investigate two distinct domains involving Monte Carlo analysis on the Pantheon Superovae Ia data, H(z) and shift parameter measurements. We conclude that the (2,1) Padé approximation is statistically the optimal approach to explain low and high-redshift data, together with the fifth-order y 2 -parametrization. At high redshifts, the (3,2) Padé approximation cannot be fully excluded, while the (2,2) Padé one is essentially ruled out.

A recent analysis of supernova Ia (SN Ia) data claims a "marginal" (∼3σ) evidence for a cosmic acceleration. This result has been complemented with a non-accelerating R h = ct cosmology, which was presented as a valid alternative to the ΛCDM model. In this paper we use the same analysis to show that non-marginal evidence for acceleration is truly found. We compare the standard Friedmann models to the R h = ct cosmology by complementing SN Ia data with baryon acoustic oscillations, gamma ray bursts, and observational Hubble datasets. We also study the power-law model, which is a functional generalisation of R h = ct. We find that the evidence for late-time acceleration cannot be refuted at a 4.56σ confidence level from SN Ia data alone, and at an even stronger confidence level (5.38σ) from our joint analysis. In addition, the non-accelerating R h = ct model fails to statistically compare with the ΛCDM, having a ∆(AIC) ∼ 30.

We here propose a new class of barotropic factor for matter, motivated by properties of isotropic deformations of crystalline solids. Our approach is dubbed Anton-Schmidt's equation of state and provides a non-vanishing, albeit small, pressure term for matter. The corresponding pressure is thus proportional to the logarithm of universe's volume, i.e. to the density itself since V ∝ ρ −1 . In the context of solid state physics, we demonstrate that by only invoking standard matter with such a property, we are able to frame the universe speed up in a suitable way, without invoking a dark energy term by hand. Our model extends a recent class of dark energy paradigms named logotropic dark fluids and depends upon two free parameters, namely n and B. Within the Debye approximation, we find that n and B are related to the Grüneisen parameter and the bulk modulus of crystals. We thus show the main differences between our model and the logotropic scenario, and we highlight the most relevant properties of our new equation of state on the background cosmology. Discussions on both kinematics and dynamics of our new model have been presented. We demonstrate that the ΛCDM model is inside our approach, as limiting case. Comparisons with CPL parametrization have been also reported in the text. Finally, a Monte Carlo analysis on the most recent low-redshift cosmological data allowed us to place constraints on n and B. In particular, we found n = −0.147 +0.113 −0.107 and B = 3.54 × 10 −3 .

Standard sirens are the gravitational wave (GW) analog of the astronomical standard candles, and can provide powerful information about the dynamics of the Universe. In this work, we simulate a catalog with 1000 standard siren events from binary neutron star mergers, within the sensitivity predicted for the third generation of the ground GW detector called Einstein telescope. After correctly modifying the propagation of GWs as input to generate the catalog, we apply our mock data set on scalar-tensor theories where the speed of GW propagation is equal to the speed of light. As a first application, we find new observational bounds on the running of the Planck mass, when considering appropriate values within the stability condition of the theory, and we discuss some consequences on the amplitude of the running of the Planck mass. In the second part, we combine our simulated standard sirens catalog with other geometric cosmological tests (Supernovae Ia and cosmic chronometers measurements) to constrain the Hu-Sawicki f (R) gravity model. We thus find new and non-null deviations from the standard ΛCDM model, showing that in the future the f (R) gravity can be tested up to 95% confidence level. The results obtained here show that the statistical accuracy achievable by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can provide strong observational bounds on modified gravity theories. 95.36.+x, 04.50.Kd, 04.30.Nk

Context. We test the theoretical predictions of several cosmological models against different observables to compare the indirect estimates of the current expansion rate of the Universe determined from model fitting with the direct measurements based on Cepheids data published recently. Aims. We perform a statistical analysis of type Ia supernova (SN Ia), Hubble parameter, and baryon acoustic oscillation data. A joint analysis of these datasets allows us to better constrain cosmological parameters, but also to break the degeneracy that appears in the distance modulus definition between H 0 and the absolute B-band magnitude of SN Ia, M 0 . Methods. From the theoretical side, we considered spatially flat and curvature-free ΛCDM, wCDM, and inhomogeneous Lemaître-Tolman-Bondi (LTB) models. To analyse SN Ia we took into account the distributions of SN Ia intrinsic parameters. Results. For the ΛCDM model we find that Ω m = 0.35 ± 0.02, H 0 = (67.8 ± 1.0) km s −1 /Mpc, while the corrected SN absolute magnitude has a normal distribution N(19.13, 0.11). The wCDM model provides the same value for Ω m , while H 0 = (66.5 ± 1.8) km s −1 /Mpc and w = −0.93 ± 0.07. When an inhomogeneous LTB model is considered, the combined fit provides H 0 = (64.2 ± 1.9) km s −1 /Mpc. Conclusions. Both the Akaike information criterion and the Bayes factor analysis cannot clearly distinguish between ΛCDM and wCDM cosmologies, while they clearly disfavour the LTB model. For the ΛCDM, our joint analysis of the SN Ia, the Hubble parameter, and the baryon acoustic oscillation datasets provides H 0 values that are consistent with cosmic microwave background (CMB)-only Planck measurements, but they differ by 2.5σ from the value based on Cepheids data.

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parameterize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the JLA supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.