How delicate are the $f(R)$ gravity models with disappearing cosmological constant?

TL;DR

This paper examines the stability issues of a specific $f(R)$ gravity model in the context of compact objects, revealing fine-tuning problems and proposing a new mass scale to ensure stability within neutron stars.

Contribution

It identifies the fine-tuning problem in Starobinsky's $f(R)$ model for neutron stars and suggests a cutoff on scalar mass to improve stability.

Findings

Severe fine tuning is required for $f(R)$ models in neutron stars.

Introducing a scalar mass cutoff can mitigate stability issues.

A new mass scale related to neutron star density is necessary.

Abstract

We consider stability of spherically symmetric solutions in $f(R)$ gravity model proposed by Starobinsky. We find that the model suffers from a severe fine tuning problem when applied to compact objects like neutron stars. The problem can be remedied by introducing a cut off on the mass of the scalar degree of freedom present in the model. A new mass scale associated with neutron stars density is then required for the stabilities of $f(R)$ gravity solutions inside relativistic stars.