Encoding cosmological futures with conformal structures

TL;DR

This paper develops a new mathematical framework using conformal structures to encode the possible futures of the universe, extending the existing initial state framework to include anisotropic and irregular cosmological end states.

Contribution

It introduces novel definitions for anisotropic future end states and singularities, expanding the formalism of quiescent cosmology to encompass the universe's potential futures.

Findings

Defined Anisotropic Future Endless Universe and Anisotropic Future Singularity.

Compared irregular conformal structures with isotropic singularities.

Proposed a complete formalization of quiescent cosmology including future states.

Abstract

Quiescent cosmology and the Weyl curvature hypothesis possess a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary to also encode appropriate cosmological futures. In order to devise a new framework we analyse the relation between regular conformal structures and (an)isotropy, the behaviour and role of a monotonic conformal factor which is a function of cosmic time, as well as four example cosmologies for further guidance. Finally, we present our new definitions of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity which offer a promising realisation for the new framework. Their irregular, degenerate conformal structures differ significantly from those of the Isotropic Singularity. The combination of the three definitions together could then provide the first complete formalisation of the quiescent cosmology concept. For completeness we also present the new definitions of an Isotropic Future Singularity and a Future Isotropic Universe. The relation to other approaches, in particular to the somewhat dual dynamical systems approach, and other asymptotic scenarios is briefly discussed.