Cosmological constraints on viable $f(R)$ models using weak lensing

TL;DR

This paper uses weak lensing data to test and constrain viable $f(R)$ gravity models, finding that standard cosmological parameters remain consistent with $ ext{Lambda}$CDM, while placing bounds on model-specific parameters.

Contribution

It introduces a Bayesian framework with MGCobaya to analyze the impact of $f(R)$ models on weak lensing observables, providing new constraints on these theories.

Findings

Standard cosmological parameters are consistent with $ ext{Lambda}$CDM for all models.

Model-dependent constraints are placed on $f(R)$ parameters.

Weak lensing effectively tests deviations from General Relativity.

Abstract

The accelerated expansion of the Universe remains one of the central open problems in modern cosmology. While the $\Lambda$CDM model successfully describes a wide range of observations, the physical nature of dark energy is still unknown, motivating the study of alternative theories of gravity. Among these, $f(R)$ models provide a well-established extension of General Relativity, capable of reproducing a $\Lambda$CDM-like background evolution without introducing an explicit dark energy component. However, they can induce deviations in the growth of cosmic structures, making them testable through observables sensitive to cosmological perturbations. In this work, we use weak gravitational lensing to constrain several viable $f(R)$ gravity models. We analyze their impact on the matter power spectrum, as well as on the convergence and cosmic shear power spectra. Our analysis is carried out within a Bayesian framework using the \textit{Cobaya} code and its modified gravity extension, \textit{MGCobaya}, which enables consistent theoretical predictions and their comparison with current weak lensing and CMB lensing data. We find that standard cosmological parameters remain consistent with the $\Lambda$CDM scenario for all models considered, as expected from their background degeneracy. Nevertheless, we obtain non-trivial and model-dependent constraints on the characteristic parameters of several $f(R)$ theories.