Constraints on the exponential $f(R)$ model from latest Hubble parameter measurements

TL;DR

This paper constrains an exponential $f(R)$ gravity model using recent Hubble parameter data, supernovae, BAO, and CMB measurements, finding parameter bounds and analyzing cosmic evolution, but cannot distinguish it from $\\Lambda$CDM with current data.

Contribution

It provides observational bounds on the exponential $f(R)$ gravity model using multiple cosmological datasets and analyzes its cosmic evolution.

Findings

Bounds on model parameters: $0.240<\Omega_m^0<0.296$, $\beta>1.47$ at 1$\sigma$

Transition redshift $z_T$ approximately 0.77

Current data cannot distinguish exponential $f(R)$ from $\Lambda$CDM

Abstract

We investigate the viable exponential $f(R)$ gravity in the metric formalism with $f(R)=-\beta R_s (1-e^{-R/R_s})$. The latest sample of the Hubble parameter measurements with 23 data points is used to place bounds on this $f(R)$ model. A joint analysis is also performed with the luminosity distances of Type Ia supernovae and baryon acoustic oscillations in the clustering of galaxies, and the shift parameters from the cosmic microwave background measurements, which leads to $0.240<\Omega_m^0<0.296$ and $\beta>1.47$ at 1$\sigma$ confidence level. The evolutions of the deceleration parameter $q(z)$ and the effective equations of state $\omega_{de}^{eff}(z)$ and $\omega_{tot}^{eff}(z)$ are displayed. By taking the best-fit parameters as prior values, we work out the transition redshift (deceleration/acceleration) $z_T$ to be about 0.77. It turns out that the recent observations are still unable to distinguish the background dynamics in the $\Lambda$CDM and exponential $f(R)$ models.