Singularity-free Cosmological Solutions with Non-rotating Perfect Fluids

TL;DR

This paper proves that all singularity-free solutions with non-rotating perfect fluids are already known, by deriving conditions necessary for non-singularity rather than constructing new solutions.

Contribution

It introduces a novel approach by deriving conditions for singularity-free solutions without explicitly finding new solutions, focusing on the constraints needed for non-singularity.

Findings

All singularity-free solutions are previously known.

Derived conditions necessary for non-singularity.

No new solutions are constructed in the study.

Abstract

The paper establishes the result that solutions of the type described in the title of the article are only those that have been already presented in the literature. The procedure adopted in the paper is somewhat novel - while the usual practice is to display an exact solution and then to examine whether it is singularity free, the present paper discovers the conditions which a singularity free solution of the desired type must satistfy. There is no attempt to obtain exact solutions. Simply, the conditions that were ad-hoc introduced in the deduction of singularity free solutions are here shown to follow from the requirement of non-singularity.