The Hubble constant (H 0) tension between Type Ia supernovae (SNe Ia) and Planck measurements ranges from 4 to 6σ. To investigate this tension, we estimate H 0 in the ΛCDM and w 0 w a CDM (cold dark matter) models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20, and 40 bins. We fit the extracted H 0 values with a function mimicking the redshift evolution: g ( z ) = H 0 ( z ) = H ˜ 0 / ( 1 + z ) α , where α indicates an evolutionary parameter and H ˜ 0 = H 0 at z = 0. We set the absolute magnitude of SNe Ia so that H 0 = 73.5 km s − 1 Mpc − 1 , and we fix fiducial values for Ω 0 m Λ CDM = 0.298 and Ω 0 m w 0 w a CDM = 0.308 . We find that H 0 evolves with redshift, showing a slowly decreasing trend, with α coefficients consistent with zero only from 1.2 to 2.0σ. Although the α coefficients are compatible with zero in 3σ, this however may affect cosmological results. We measure locally a variation of H 0 ( z = 0 ) − H 0 ( z = 1 ) = 0.4 km s − 1 Mpc − 1 in three and four bins. Extrapolating H 0 ( z ) to z = 1100, the redshift of the last scattering surface, we obtain values of H 0 compatible in 1σ with Planck measurements independent of the cosmological models and number of bins we investigated. Thus, we have reduced the H 0 tension in the range from 54% to 72% for both cosmological models. If the decreasing trend of H 0 ( z ) is real, it could be due to astrophysical selection effects or to modified gravity.

The difference from 4 to 6 σ in the Hubble constant (H0) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (Cosmic Microwave Background obtained by the Planck data) still challenges the astrophysics and cosmology community. Previous analysis has shown that there is an evolution in the Hubble constant that scales as f(z)=H0/(1+z)η, where H0 is H0(z=0) and η is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the Baryon Acoustic Oscillations. We assume H0=70kms−1Mpc−1 as the local value and divide the Pantheon into three bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously (H0, Ω0m in the ΛCDM model and H0, wa in the w0waCDM model), for each bin we implement a Markov-Chain Monte Carlo analysis (MCMC) obtaining the value of H0 assuming Gaussian priors to restrict the parameters spaces to values we expect from our prior knowledge of the current cosmological models and to avoid phantom Dark Energy models with w<−1. Subsequently, the values of H0 are fitted with the model f(z). Our results show that a decreasing trend with η∼10−2 is still visible in this sample. The η coefficient reaches zero in 2.0 σ for the ΛCDM model up to 5.8 σ for w0waCDM model. This trend, if not due to statistical fluctuations, could be explained through a hidden astrophysical bias, such as the effect of stretch evolution, or it requires new theoretical models, a possible proposition is the modified gravity theories, f(R). This analysis is meant to further cast light on the evolution of H0 and it does not specifically focus on constraining the other parameters. This work is also a preparatory to understand how the combined probes still show an evolution of the H0 by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the Ω0m comparable with the ones achieved through SNe Ia.

We analyze the f(R) gravity in the so-called Jordan frame, as implemented to the isotropic Universe dynamics. The goal of the present study is to show that, according to recent data analyses of the supernovae Ia Pantheon sample, it is possible to account for an effective redshift-dependence of the Hubble constant. This is achieved via the dynamics of a non-minimally coupled scalar field, as it emerges in the f(R) gravity. We face the question both from an analytical and purely numerical point of view, following the same technical paradigm. We arrive to establish that the expected decay of the Hubble constant with the redshift z is ensured by a form of the scalar field potential, which remains essentially constant for z ≲ 0.3, independently if this request is made a priori, as in the analytical approach, or obtained a posteriori, when the numerical procedure is addressed. Thus, we demonstrate that an f(R) dark energy model is able to account for an apparent variation of the Hubble constant due to the rescaling of the Einstein constant by the f(R) scalar mode.

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.

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We focus on weak inhomogeneous models of the Universe at low redshifts, described by the Lemaître-Tolman-Bondi (LTB) metric. The principal aim of this work is to compare the evolution of inhomogeneous perturbations in the ΛCDM cosmological model and f (R) modified gravity theories, considering a flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric for the background. More specifically, we adopt the equivalent scalar-tensor formalism in the Jordan frame, in which the extra degree of freedom of the f (R) function is converted into a non-minimally coupled scalar field. We investigate the evolution of local inhomogeneities in time and space separately, following a linear perturbation approach. Then, we obtain spherically symmetric solutions in both cosmological models. Our results allow us to distinguish between the presence of a cosmological constant and modified gravity scenarios, since a peculiar Yukawa-like solution for radial perturbations occurs in the Jordan frame. Furthermore, the radial profile of perturbations does not depend on a particular choice of the f (R) function, hence our results are valid for any f (R) model.