Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

TL;DR

This paper investigates $f(R)$ gravity theories by calculating key parameters and applying observational constraints from solar system, cosmology, and binary pulsar systems to test their viability.

Contribution

It provides a comprehensive analysis of $f(R)$ gravity models using a scalar-tensor representation with the chameleon mechanism, deriving constraints from multiple observational regimes.

Findings

Constraints on $f(R)$ model parameters from solar system tests.

Limits on $f(R)$ models based on binary pulsar orbital decay.

Compatibility of specific $f(R)$ models with cosmological observations.

Abstract

The $f(R)$ gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general $f(R)$ gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parameterized post-Newtonian parameters $\gamma$ and $\beta$, the effective gravitational constant $G_{\rm eff}$, and the effective cosmological constant $\Lambda_{\rm eff}$. In addition, for the general $f(R)$ gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific $f(R)$ models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.