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

The accelerated expansion of the Universe remains one of the central open problems in modern cosmology. While the $Λ$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 $Λ$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 $Λ$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.

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