Energy Density Inhomogeneities with Polynomial $f(R)$ Cosmology

TL;DR

This paper investigates how polynomial $f(R)$ gravity models influence the stability of energy density homogeneity in self-gravitating spherical objects, considering various physical factors and their interplay.

Contribution

It introduces evolution equations linking the Weyl tensor with matter parameters to analyze density inhomogeneities in polynomial $f(R)$ gravity.

Findings

Shear, pressure, and dissipative effects influence density inhomogeneity.

$f(R)$ terms affect the stability of energy density homogeneity.

Multiple factors collectively determine the inhomogeneity in different fluid models.

Abstract

In this paper, we study the effects of polynomial $f(R)$ model on the stability of homogeneous energy density in self-gravitating spherical stellar object. For this purpose, we construct couple of evolution equations which relate the Weyl tensor with matter parameters. We explore different factors responsible for density inhomogeneities with non-dissipative dust, isotropic as well as anisotropic fluids and dissipative dust cloud. We find that shear, pressure, dissipative parameters and $f(R)$ terms affect the existence of inhomogeneous energy density.