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

TL;DR

This study tests the viability of several viable $f(R)$ gravity models by confronting their growth and lensing predictions with current weak-lensing and CMB-lensing data. Using a Bayesian framework with Cobaya and the modified gravity extension MGCobaya, the authors compute convergence and cosmic shear power spectra under models such as Hu–Sawicki, Starobinsky, and additional forms designed to mimic ΛCDM background. They find that standard cosmological parameters remain consistent with ΛCDM across all models, but the characteristic $f(R)$ parameters are constrained in a model-dependent way, with some models yielding strong upper limits while others remain poorly constrained. The results underscore the model dependence of tests of modified gravity and demonstrate that weak lensing, especially the convergence spectrum, is a sensitive discriminator of growth modifications in $f(R)$ theories.

Abstract

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.

Figures (12)

• Figure 1: Matter power spectra for $\Lambda$CDM and $f(R)$ models at $z=0$. We fixed values for $f(R)$ parameters according to the priors indicated in Table \ref{['tab:priors']}. We set $f_{R0}=10^{-5}$, $\xi=10^{-10}$, $w=10^{-6}$ and $b=5 \cdot 10^{-5}$. All of the $f(R)$ models show an increase in the amplitudes of the spectra, especially at nonlinear scales.
• Figure 2: Power matter spectra ratio to $\Lambda$CDM. The $f(R)$ models present deviations with respect to $\Lambda$CDM that range around from $10\%$ (small power) to $200\%$ (logarithmic). For Starobinsky and logarithmic deviations is notorious inclusive for scales from $k\sim 10^{-3}-10^{-4}$$h Mpc^{-1}$.
• Figure 3: Convergence power spectra for $\Lambda$CDM and $f(R)$ models. We took the same values for the parameters as in the matter power spectrum of Figure \ref{['fig:matterpower']}. Weak lensing amplifies the differences between $f(R)$ models and $\Lambda$CDM, making the departures especially for the logarithmic and Starobinsky cases, clearly visible across all multipoles.
• Figure 4: Convergence spectra ratio to $\Lambda$CDM. The convergence spectra ratios make the hierarchy of departures from $\Lambda$CDM clearly visible, with large deviations for Starobinsky and logarithmic models and progressively milder ones for the remaining $f(R)$.
• Figure 5: CMB lensing potential power spectra for $\Lambda$CDM and $f(R)$ models. We took the same values for the parameters as in the matter and convergence power spectra (Figures \ref{['fig:matterpower']} and \ref{['fig:relation_matterpower']}, respectively). The behaviour obtained is consistent with that of the convergence spectra, in terms of the relative ordering of the models, the amplitudes of the lensing potential spectrum, and the multipole scales at which the effects appear.