Late-time cosmology in a model of modified gravity with an exponential function of the curvature

TL;DR

This paper investigates a specific exponential $f(R)$ gravity model's ability to describe late-time cosmic acceleration, demonstrating its consistency with observational data and comparing its predictions with the $ ext{Lambda}$CDM model.

Contribution

It introduces and analyzes a novel exponential $f(R)$ gravity model, providing numerical solutions and observational constraints to validate its viability for late-time cosmology.

Findings

Model's parameters fit well with Planck 2018 data

Predicted cosmological parameters align with $ ext{Lambda}$CDM values

Model offers a viable alternative explanation for cosmic acceleration

Abstract

In this work, we analyse the late-time evolution of the universe for a particular $f(R)$ gravity model built from an exponential function of the scalar curvature. Following the literature, we write the field equations in terms of a suited statefinder function ($y_H(z)$) and considering well motivated physical initial conditions, the resulting equations are solved numerically. Also, the cosmological parameters $w_{\rm{DE}}$, $w_{\rm{eff}}$, $\Omega_{\rm{DE}}$ and $H(z)$ and the statefinder quantities $q$, $j$, $s$ and $Om(z)$ are explicitly expressed in terms of $y_H(z)$ and its derivatives. Furthermore, setting an appropriate set of values for the model parameters, the cosmological parameters as well as the statefinder quantities are plotted, and their present values (at $z=0$), are shown to be compatible with Planck 2018 observations and the $\Lambda$CDM-model values. Considering updated measurements from the dynamics of the expansion of the universe, $H(z)$, we perform an statistical analysis to constrain the free parameters of the model, finding a particular set of values that fit the data well and predict acceptable values for the cosmological and statefinder parameters at present time. Therefore, the $f(R)$ gravity model is found to be consistent with the considered observational data, and a viable alternative to explain the late-time acceleration of the universe.