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

TL;DR

This study constrains a modified gravity model with an exponential curvature function using observational data, finding significant deviation from standard cosmology and showing it can fit current cosmological observations.

Contribution

It provides the first detailed statistical analysis of an exponential $f(R)$ gravity model using multiple observational datasets, demonstrating its viability as an alternative to $\Lambda$CDM.

Findings

The parameter $b$ deviates from zero at >3.5 sigma, indicating a significant departure from $\Lambda$CDM.

The model predicts a current $H_0$ value between Planck and SH0ES measurements.

An oscillatory dark energy equation of state suggests deviations from the standard model.

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.