Observational constraints on a modified-gravity model with an exponential function of the curvature using the expansion history, the RSD, and the Pantheon+SH0ES data

Abstract: Considering a well-motivated $f(R)$ modified-gravity model, in which an exponential function of the curvature is included, in this paper we implement a statistical data analysis to set constraints on the parameters of the model, taking into account an analytic approximate solution for the expansion rate, $H(z)$. Using a Monte Carlo Markov Chain-based analysis of the expansion rate evolution, the standardized SN distance modulus and the redshift space distortion observational data, we find that the preferred value for the perturbative parameter, $b$, quantifying the deviation of the $f(R)$ model from $\Lambda$CDM, lies in a region that excludes $b = 0$ at $\gtrsim 3.5 \sigma$ C.L., and that the predicted current value of the Hubble parameter, $H_0$, locates in between the two observational results currently under scrutiny from Planck and SH0ES collaborations. Under the implemented approximate solution, and with the constraints obtained for the parameters, the proposed $f(R)$ model successfully reproduces the observational data and the predicted evolution of interesting cosmological parameters resemble the results of $\Lambda$CDM, as expected, while an oscillatory behavior of the dark energy equation of state is observed, pointing to deviation from the concordance cosmological model. The results presented here reinforce the conclusion that the $f(R)$ modified-gravity model represents a viable alternative to describe the evolution of the Universe, avoiding the challenges faced by $\Lambda$CDM.