Cosmological Constraints from Hubble Parameter on f(R) Cosmologies

TL;DR

This paper uses Hubble parameter data from differential age methods, combined with BAO and CMB constraints, to place bounds on f(R) gravity parameters, showing these models can replicate cosmic history without dark energy.

Contribution

It provides observational bounds on f(R) = R - β/R^n gravity in the Palatini approach using multiple cosmological data sets.

Findings

Bounds on n and β consistent with other analyses

f(R) models can reproduce cosmic evolution phases

No dark energy needed for certain parameter ranges

Abstract

Modified $f(R)$ gravity in the Palatini approach has been presently applied to Cosmology as a realistic alternative to dark energy. In this concern, a number of authors have searched for observational constraints on several $f(R)$ gravity functional forms using mainly data of type Ia supenovae (SNe Ia), Cosmic Microwave Background ({\rm CMB}) radiation and Large Scale Structure ({\rm LSS}). In this paper, by considering a homogeneous and isotropic flat universe, we use determinations of the Hubble function $H(z)$, which are based on differential age method, to place bounds on the free parameters of the $f(R) = R - \beta/R^{n}$ functional form. We also combine the $H(z)$ data with constraints from Baryon Acoustic Oscillations ({\rm BAO}) and {\rm CMB} measurements, obtaining ranges of values for $n$ and $\beta$ in agreement with other independent analyses. We find that, for some intervals of $n$ and $\beta$, models based on $f(R) = R - \beta/R^{n}$ gravity in the Palatini approach, unlike the metric formalism, can produce the sequence of radiation-dominated, matter-dominated, and accelerating periods without need of dark energy.