High-redshift cosmography: auxiliary variables versus Padé polynomials

Abstract

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.

Modeling of Accelerating Universe with Bulk Viscous Fluid in Bianchi V Space‐Time

“…This value is quite closer to that constrained by Capozziello et al. [75]. From a joint analysis of the data and the Pantheon compilation data, the Hubble parameter H 0 is obtained to be which sits in a range middle to the observed Hubble tension.…”

“…Capozziello et al. [ 75 ] have also obtained a slightly larger value of j than the value predicted by concordance paradigm. Mukherjee and Banerjee in their work, [ 82 ] concluded that, any deviation of the jerk parameter from the ΛCDM value indicates an interaction between the dark energy and dark matter.…”

“…[ 74 ] Using our anisotropic model, the present value of deceleration parameter is computed as which is quite closer to the values constrained in a recent work. [ 75 ] The transit redshift can be translated into cosmic time through the time red‐shift relation as described in above subsection. In fact, from our present analysis, we infer that, the deceleration to acceleration has occurred around 5.9 Gyrs from now.…”

Non-parametric reconstruction of the cosmological jerk parameter

“…Surely the parameters made out of even higher derivatives like snap (4th order derivative of a), crack (5th order derivative) etc. could well be evolving [78]. But we focus on j which is the evolution of q, the highest order derivative that is an observationally measured quantity.…”

A new comparison between holographic dark energy and standard $$\varLambda $$-cosmology in the context of cosmography method

“…3). As a well-known method in cosmology, cosmography method has been widely used in the literature [37][38][39][40][41][42][43][44][45][46][47]. This method was first proposed by [37] and [38] to distinguish between various dark energy models.…”