Running Hubble constant from the SNe Ia Pantheon sample?

Abstract

The mismatch between different independent measurements of the expansion rate of the Universe is known as the Hubble constant (H0) tension, and it is a serious and pressing problem in cosmology. We investigate this tension considering the dataset from the Pantheon sample, a collection of 1048 Type Ia Supernovae (SNe Ia) with a redshift range 0 < z < 2.26. We perform a binned analysis in redshift to study if the H0 tension also occurs in SNe Ia data. Hence, we build equally populated subsamples in three and four bins, and we estimate H0 in each bin considering the ΛCDM and w0waCDM cosmological models. We perform a statistical analysis via a Markov Chain Monte Carlo (MCMC) method for each bin. We observe that H0 evolves with the redshift, using a fit function H0(z) = H0(1 + z) −α with two fitting parameters α and H0. Our results show a decreasing behavior of H0 with α ∼ 10 −2 and a consistency with no evolution between 1.2 σ and 2.0 σ. Considering the H0 tension, we extrapolate H0(z) until the redshift of the last scattering surface, z = 1100, obtaining values of H0 consistent in 1 σ with the cosmic microwave background (CMB) measurements by Planck. Finally, we discuss possible f (R) modified gravity models to explain a running Hubble constant with the redshift, and we infer the form of the scalar field potential in the dynamically equivalent Jordan frame.

A Critical Discussion on the H0 Tension

“…A popular approach to address these issues is to consider extensions of ΛCDM model and GR. As previously mentioned, f (R) gravity [29] and other modified theories [17,39] have been applied for various cosmological and astrophysical tests [17,39,82,84,85,219,220].…”

“…A recent research line explores the possibility of a "variable H 0 constant", i.e., the idea that the measured value of the Hubble constant might depend on the redshift (i.e., the scale) at which it is measured [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]. In this context, the H 0 constant can be evaluated by the look-back time [90].…”

“…In this context, a dependence of H 0 on the redshift has been observed in real SNe Ia data and interpreted through the f (R) gravity formalism [81][82][83][84][85]88]. More specifically, in [81], a functional form…”

“…To accomplish this issue, one not only needs to provide definitive evidence of peculiar effects beyond the ΛCDM model, but also to build up an appropriate extension of the standard framework containing not only novel ideas to solve the H 0 and other tensions but also retaining the outstanding success achieved by GR and ΛCDM model when they are compared with observations. As said, a novel approach considers the possibility of an evolution of H 0 constant with redshift as a way to address the tension [75][76][77][78][79][80][81][82][83][84][85][86][87][88]. In this sense, the evolution of H 0 and the corresponding tension are considered as a sort of "diagnostics" of a symptom of the breaking-down of the ΛCDM model (or even of the FLRW metric, because it would suggest, according to this interpretation, that the parameterization H(z) = H 0 E(z) is not working), marking the points in which observations are not consistent with the model [75][76][77][78][79][80].…”

New Parametrization of the Dark-Energy Equation of State with a Single Parameter

“…As we will see, apart from being capable of fitting the data, the new parametrization can partially alleviate the H 0 tension too since it leads to a H 0 value in between the Planck one and the one from direct measurements [59,60]. Recently, several authors have conducted so many remarkable works regarding the measurements of H 0 obtained from cosmological probes for different redshifts, such as a bias-free cosmological analysis with quasars alleviating H 0 tension [61]; new statistical insights and cosmological constraints consisting of gamma-ray bursts, quasars, baryonic acoustic oscillations, and supernovae Ia [62]; reduced uncertainties up to 43% on the Hubble constant and the matter density with the SNIa with a new statistical analysis [63]; on the Hubble constant tension in the SNIa Pantheon sample [64]; on the evolution of the Hubble constant with the SNIa Pantheon sample and baryon acoustic oscillations: a feasibility study for GRB-cosmology in 2030 [65]; and f (R) gravity in the Jordan frame as a paradigm for the Hubble tension, in which the authors provides a subsequent interpretation of the results through an effective Hubble constant that evolves with the redshift in a f (R) modified gravity theory in the Jordan frame [66].…”