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We investigate the Hubble constant tension within $f(R)$ modified gravity in the Jordan frame, focusing on its application to the dynamics of an isotropic Universe. A scalar field, non-minimally coupled to the metric, provides an extra degree of freedom compared to General Relativity. We analyze the impact of such a scalar field on the cosmic expansion, leading to an effective Hubble constant $H_{0}^{\text{eff}}(z)$, dependent on redshift $z$. We show that our $f(R)$ model might mimic dark energy and provide an apparent variation of the Hubble constant. Our results align with recent cosmological data analysis in redshift bins, indicating a decreasing trend of the Hubble constant. The redshift dependence of $H_{0}^{\text{eff}}(z)$ might potentially reconcile measurements of the Hubble constant from probes at different redshifts., Comment: 6 pages, 1 figure, contribution to IFAE 2024, Florence (Italy), 3-5 April 2024

Starting from a recently proposed framework for the evaluation of the cosmological averages, we evaluate the higher-order moments for the distribution of a given observable. Then, we explicitly discuss the case of the Hubble-Lema\^itre diagram and evaluate its skewness at the leading order in the cosmological perturbative expansion of the gravitational potential. In particular, we focus on perturbations of the luminosity distance due to gravitational lensing. Finally, we discuss our findings in view of recent numerical relativistic simulations, confirming that the skewness in the Hubble-Lema\^itre diagram primarily originates from the late-time matter bispectrum, with other line-of-sight projection effects being sub-dominant., Comment: 32 pages, 4 figures, references added, discussions improved, conclusions unchanged

The Hubble constant ($H_0$) tension is one of the major open problems in modern cosmology. This tension is the discrepancy, ranging from 4 to 6 $\sigma$, between the $H_0$ value estimated locally with the combination of Supernovae Ia (SNe Ia) + Cepheids and the cosmological $H_0$ obtained through the study of the Cosmic Microwave Background (CMB) radiation. The approaches adopted in Dainotti et al. 2021 (ApJ) and Dainotti et al. 2022 (Galaxies) are introduced. Through a binning division of the Pantheon sample of SNe Ia (Scolnic et al. 2018), the value of $H_0$ has been estimated in each of the redshift-ordered bins and fitted with a function lowering with the redshift. The results show a decreasing trend of $H_0$ with redshift. If this is not due to astrophysical biases or residual redshift evolution of the SNe Ia parameters, it can be explained in light of modified gravity theories, e.g., the $f(R)$ scenarios. We also briefly describe the possible impact of high-$z$ probes on the Hubble constant tension, such as Gamma-ray bursts (GRBs) and Quasars (QSOs), reported in Dainotti et al. 2022 (Galaxies) and Lenart et al. 2022 (ApJ), respectively., Comment: 60 pages, 4 figures, 7 panels, PoS 2022 proceeding

We analyze inhomogeneous cosmological models in the local Universe, described by the Lema\^itre-Tolman-Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the $\Lambda$LTB model, in which the cosmological constant $\Lambda$ is included in the LTB formalism, with inhomogeneous cosmological models based on $f\left(R\right)$ modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of $f\left(R\right)$ gravity. While radial perturbations follow a power-law in the $\Lambda$LTB model, Yukawa-like contributions appear in the $f\left(R\right)$ theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the $f\left(R\right)$ functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect., Comment: 31 pages, 5 figures, updated to match published version

We analyse 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 $z\lesssim0.3$, 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., Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letters (manuscript version after the proof corrections)

The mismatch between different independent measurements of the expansion rate of the Universe is known as the Hubble constant ($H_0$) 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

The difference from 4 to 6 $\sigma$ in the Hubble constant ($H_0$) between the values observed with the local (Cepheids and Supernovae Ia, SNe Ia) and the high-z probes (CMB 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 $f(z)=\mathcal{H}_{0}/(1+z)^{\eta}$, where $\mathcal{H}_0$ is $H_{0}(z=0)$ and $\eta$ is the evolutionary parameter. Here, we investigate if this evolution still holds by using the SNe Ia gathered in the Pantheon sample and the BAOs. We assume $H_{0}=70 \textrm{km s}^{-1}\textrm{Mpc}^{-1}$ as the local value and divide the Pantheon into 3 bins ordered in increasing values of redshift. Similar to our previous analysis but varying two cosmological parameters contemporaneously ($H_0$, $\Omega_{0m}$ in the $\Lambda$CDM model and $H_0$, $w_a$ in the $w_{0}w_{a}$CDM model), for each bin we implement a MCMC analysis obtaining the value of $H_0$ $[...]$. Subsequently, the values of $H_0$ are fitted with the model $f(z)$. Our results show that a decreasing trend with $\eta \sim10^{-2}$ is still visible in this sample. The $\eta$ coefficient reaches zero in 2.0 $\sigma$ for the $\Lambda$CDM model up to 5.8 $\sigma$ for $w_{0}w_{a}$CDM 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 work is also a preparatory to understand how the combined probes still show an evolution of the $H_0$ by redshift and what is the current status of simulations on GRB cosmology to obtain the uncertainties on the $\Omega_{0m}$ comparable with the ones achieved through SNe Ia., Comment: 45 pages, 6 figures, 3 tables, added references, final version after proofs corrections, published in Galaxies

We focus on weak inhomogeneous models of the Universe at low redshifts, described by the Lema\^itre-Tolman-Bondi (LTB) metric. The principal aim of this work is to compare the evolution of inhomogeneous perturbations in the $\Lambda$CDM cosmological model and $f(R)$ modified gravity theories, considering a flat Friedmann-Lema\^itre-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., Comment: 9 pages, 3 figures, Proceedings of the 16th Marcel Grossmann Meeting (5-10 July 2021). Talk presented in the parallel session "Dark Energy and the Accelerating Universe"

The Hubble constant ($H_0$) tension between Type Ia Supernovae (SNe Ia) and Planck measurements ranges from 4 to 6 $\sigma$. To investigate this tension, we estimate $H_{0}$ in the $\Lambda$CDM and $w_{0}w_{a}$CDM 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: $g(z)={H_0}(z)=\tilde{H}_0/(1+z)^\alpha$, where $\alpha$ indicates an evolutionary parameter and $\tilde{H}_0=H_0$ at $z=0$. We set the absolute magnitude of SNe Ia so that $H_0=73.5\,\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$, and we fix fiducial values for $\Omega_{0m}^{\Lambda CDM}=0.298$ and $\Omega_{0m}^{w_{0}w_{a}CDM}=0.308$. We find that $H_0$ evolves with redshift, showing a slowly decreasing trend, with $\alpha$ coefficients consistent with zero only from 1.2 to 2.0 $\sigma$. Although the $\alpha$ coefficients are compatible with 0 in 3 $\sigma$, this however may affect cosmological results. We measure locally a variation of $H_0(z=0)-H_0(z=1)=0.4\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$ in 3 and 4 bins. Extrapolating ${H_0}(z)$ to $z=1100$, the redshift of the last scattering surface, we obtain values of $H_0$ compatible in 1 $\sigma$ with Planck measurements independently of cosmological models and number of bins we investigated. Thus, we have reduced the $H_0$ tension from $54\%$ to $72\%$ for the $\Lambda$CDM and $w_{0}w_{a}$CDM models, respectively. If the decreasing trend of $H_0(z)$ is real, it could be due to astrophysical selection effects or to modified gravity., Comment: 20 pages, 6 figures, 1 table; With corrected proofs and bibliography, to be published in ApJ