Conformal Structures Admitted by a Class of FRW Cosmologies

TL;DR

This paper explores the conformal structures of various FRW cosmologies within Quiescent Cosmology, identifying classes that admit isotropic conformal structures and analyzing their relation to known cosmological singularities and states.

Contribution

It demonstrates the existence of large classes of FRW models with isotropic conformal structures compatible with Quiescent Cosmology, expanding understanding of cosmological singularities and final states.

Findings

Identified FRW models with isotropic conformal structures

Compared cosmological events with conformal structures in Quiescent Cosmology

Highlighted classes of FRW solutions not fitting existing conformal structures

Abstract

In this paper we demonstrate that there are large classes of Friedmann-Robertson-Walker (FRW) cosmologies that admit isotropic conformal structures of Quiescent Cosmology. FRW models have long been known to admit singularities such as Big Bangs and Big Crunches [1, 2] but recently it has been shown that there are other cosmological structures that these solutions contain. These structures are Big Rips, Sudden Singularities and Extremality Events [1, 2]. Within the Quiescent Cosmology framework [3] there also exist structures consistent with a cosmological singularity known as the Isotropic Past Singularity (IPS) [4, 5]. There also exists a cosmological final state known as a Future Isotropic Universe (FIU) [4], which strictly speaking, doesn't fit with the fundamental ideals of Quiescent Cosmology. In this paper, we compare the cosmological events of a large class of FRW solutions to the conformal structures of Quiescent Cosmology [4]. In the first section of this paper we present the relevant background information and our motivation. In the second section of this paper we construct conformal relationships for relevant FRW models. The third section contains a thorough discussion of a class of FRW solutions that cannot represent any of the previously constructed isotropic conformal structures from Quiescent Cosmology. The final section contains our remarks and future outlook for further study of this field.