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

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, \(H(z)\). From the 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, lives in a region which excludes \(b = 0\) at \(\gtrsim 4.5 \sigma\) 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, indicating that the proposed model would alleviate the apparent tension. Under the implemented approximate solution, and with the constraints obtained for the parameters, the proposed \(f(R)\) model successfully reproduce 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 reinforces the conclusion that the \(f(R)\) modified-gravity model represents a viable alternative to describe the evolution of the Universe, evading the challenges faced by \(\Lambda\)CDM.