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Modification of general relativity (GR) inspired by theories like $f(R)$ gravity is among the most popular ones to explain the late-time acceleration of the Universe as an alternative to the $\Lambda$CDM model. In this work, we use the state-of-the-art BAO+BBN data and the most recent Type Ia supernovae (SNe Ia) sample namely PantheonPlus, including the Cepheid host distances and covariance from SH0ES samples, to robustly constrain the $f(R)$ gravity framework via two of the most popular $f(R)$ models in literature, namely, the Hu-Sawicki and Starobinsky models. Additionally, we consider how the time variation of the Newton's gravitational constant affects the supernovae distance modulus relation. We find a minor evidence for $f(R)$ gravity under the Hu-Sawicki dynamics from BAO+BBN and BAO+BBN+uncalibrated supernovae joint analysis, but the inclusion of Cepheid host distances, makes the model compatible with GR. Further, we notice tendency of this model to relax the $H_0$ tension. In general, in all the analyses carried out in this study with the late time probes, we find both the $f(R)$ models to be consistent with GR at 95\% CL., Comment: 9 pages, 3 figures, 1 table, matches the version published in Physics of Dark Universe

We investigate two new observational perspectives in the context of torsional gravitational modification of general relativity, i.e., the $f(T)$ gravity: i) We use Pantheon data of type Ia supernovae motivated by a time variation of the Newton's constant on the supernovae distance modulus relation, and find that a joint analysis with Baryon Acoustic Oscillations (BAO) and Big Bang Nucleosynthesis (BBN), i.e., Pantheon+BAO+BBN, provides constraints on the effective free parameter of the theory to be well compatible with the $\Lambda$CDM prediction; ii) We present the framework of $f(T)$ gravity at the level of linear perturbations with the phenomenological functions, namely the effective gravitational coupling $\mu$ and the light deflection parameter $\Sigma$, which are commonly used to parameterize possible modifications of the Poisson equation relating the matter density contrast to the lensing and the Newtonian potentials, respectively. We use the available Cosmic Microwave Background (CMB) data sets from the Planck 2018 release to constrain the free parameters of the $f(T)$ power-law gravity and $\Lambda$CDM models. We find that CMB data, and its joint analyses with Pantheon and BAO data constrain the $f(T)$ power-law gravity scenario to be practically indistinguishable from the $\Lambda$CDM model. We obtain the strongest limits ever reported on $f(T)$ power-law gravity scenario at the cosmological level., Comment: 13 pages, 2 tables, 6 figures; New discussions added; Matches the version published in Physical Review D

Using the latest observational data from Planck-CMB and its combination with the pre-reconstructed full-shape (FS) galaxy power spectrum measurements from the BOSS DR12 sample and eBOSS LRG DR16 sample, we report the observational constraints on the cosmic neutrino properties given by the extended $\Lambda$CDM scenario: $\Lambda$CDM + $N_{\rm eff}$ + $\sum m_{\nu}$ + $c^2_{\rm eff}$ + $c^2_{\rm vis}$ + $\xi_{\nu}$, and its particular case $\Lambda$CDM + $c^2_{\rm eff}$ + $c^2_{\rm vis}$ + $\xi_{\nu}$, where $N_{\rm eff}$, $\sum m_{\nu}$, $c^2_{\rm eff}$, $c^2_{\rm vis}$, $\xi_{\nu}$ are the effective number of species, the total neutrino mass, the sound speed in the neutrinos rest frame, the viscosity parameter and the degeneracy parameter quantifying a cosmological leptonic asymmetry, respectively. We observe that the combination of FS power spectrum measurements with the CMB data significantly improves the parametric space of the models compared to the CMB data alone case. We find no evidence for neutrinos properties other than the ones predicted by the standard cosmological theory. Our most robust observational constraints are given by CMB + BOSS analysis. For the generalized extended $\Lambda$CDM scenario, we find $c^2_{\rm eff}=0.3304^{+0.0064}_{-0.0075}$, $c^2_{\rm vis}=0.301^{+0.037}_{-0.033}$, $\xi_{\nu} < 0.05$, $N_{\rm eff}=2.90 \pm 0.15$ at 68\% CL, with $\sum m_{\nu} < 0.116$ eV at 95\% CL. These are the strongest limits ever reported for these extended $\Lambda$CDM scenarios., Comment: 22 pages, 4 figures, 3 tables; Substantial changes in the text with updated results; matches the version published in JCAP except some additional refs in this version