General cosmography model with spatial curvature

Abstract

The cosmographic approach is adopted to determine the spatial curvature (i.e., Ω K ) combining the latest released cosmic chronometers data (CC), the Pantheon sample of type Ia supernovae observations, and the baryon acoustic oscillation measurements. We use the expanded transverse comoving distance D M (z) as a basic function for deriving H(z) and the other cosmic distances. In this scenario, Ω K can be constrained only by CC data. To overcome the convergence issues at high-redshift domains, two methods are applied: the Padé approximants and the Taylor series in terms of the new redshift y = z/(1 + z). Adopting the Bayesian evidence, we find that there is positive evidence for the Padé approximant up to order (2, 2) and weak evidence for the Taylor series up to 3-rd order against ΛCDM + Ω K model. The constraint results show that a closed universe is preferred by the present observations under all the approximants used in this study. And the tension level of the Hubble constant H 0 is less than 2σ significance between different approximants and the local distance ladder determination. For each assumed approximant, H 0 is anti-correlated with Ω K and the sound horizon at the end of the radiation drag epoch, which indicates that the H 0 tension problem can be slightly relaxed by introducing Ω K or any new physics which can reduce the sound horizon in the early universe.

Connecting early and late epochs by f(z)CDM cosmography

“…The Padé series P (2, 2) proved to be unstable for high values of cosmographic parameters, although widely reliable in the selected priors used in this work. It is therefore necessary to explore new possibilities, such as Padé polinomials with different orders, which may allows for a more fast convergence of the series [47]. Alternatively, one can evaluate the possibility to use other redshift parameterizations [27,15,48] or to construct the function f (z) with other rational polynomials like the Chebyshev ones [21,46].…”

Quantifying the evidence for the current speed-up of the Universe with low and intermediate-redshift data. A more model-independent approach

“…The central value is now more compatible with the local determinations, although some criticisms to this new estimation have been also drawn [105]. It is also worth to mention the cosmologyindependent analyses carried out in [22,52,61,[106][107][108][109], where use is made of different combinations of cosmological low and intermediate-redshift data involving SnIa, CCH and BAOs. Values of H 0 lying in the range ∼ 67 − 68.5 km s −1 Mpc −1 are obtained, see these references for details.…”

“…This allows us to reconstruct the aforesaid cosmographical functions in a fairer and more model and parametrization-independent way. We hope to improve thereby the methodology applied and the constraints reported on e.g., q 0 or z t , in many other works in the literature, as those based on concrete parametrizations of the deceleration or the jerk parameters [4,6,16,, truncated cosmographical series [30,41,[44][45][46][47][48][49][50][51][52], alternative expansions of the luminosity distance [53], or specific cosmological models, including also various parametrizations of the DE density or the DE equation of state (EoS) parameter, see e.g. [1-6, 24, 49, 54-57].…”

Cosmic dissonance: are new physics or systematics behind a short sound horizon?

“…The specifications of the three polynomial parametrisations (hereafter referred to as model 1, 2 and 3) are listed in Table 1. Model 1 adopts a polynomial expansion of H(z) (Weinberg 1972;Visser 2004), model 2 expands the luminosity distance D L 1 as a polynomial in log(1 + z) (Risaliti & Lusso 2019), and model 3 describes transverse comoving distances D M by polynomials in z/(1 + z) (Cattoën & Visser 2007;Li et al 2020). For model 1, comoving distances were obtained from H(z) through direct numerical integration of…”