Delicate f(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters

TL;DR

This paper examines specific f(R) gravity models that eliminate the cosmological constant, assessing their compatibility with observational data and their ability to replicate the universe's expansion history.

Contribution

It analyzes the Hu-Sawicki, Appleby-Battye, and Starobinsky f(R) models, focusing on their observational viability and the need for parameter fine-tuning to avoid singularities.

Findings

Models pass Solar system and laboratory tests.

Some parameter choices match high-redshift universe behavior.

Variations occur in low-redshift expansion history.

Abstract

We study the $f(R)$ theory of gravity using metric approach. In particular we investigate the recently proposed model by Hu-Sawicki, Appleby $-$ Battye and Starobinsky. In this model, the cosmological constant is zero in flat space time. The model passes both the Solar system and the laboratory tests. But the model parameters need to be fine tuned to avoid the finite time singularity recently pointed in the literature. We check the concordance of this model with the $H(z)$ and baryon acoustic oscillation data. We find that the model resembles the $\Lambda$CDM at high redshift. However, for some parameter values there are variations in the expansion history of the universe at low redshift.