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

Abstract

We investigate the viable exponential f (R ) gravity in the metric formalism with f (R )=-β 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 <Ω_m⁰<0.296 and β >1.47 at the 1 σ confidence level. The evolutions of the deceleration parameter q (z ) and the effective equations of state ω_de^eff(z ) and _ω^toteff(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 Λ CDM and exponential f (R ) models.