A study of inhomogeneous massless scalar gauge fields in cosmology

TL;DR

This paper investigates the behavior of inhomogeneous massless scalar gauge fields in anisotropic cosmological models, extending Wald's no-hair theorem and identifying new self-similar solutions with implications for the universe's homogeneity.

Contribution

It extends Wald's no-hair theorem to include $j$-form fields and introduces three new self-similar solutions in anisotropic cosmologies.

Findings

Discovery of three new self-similar space-times: Edge, Rope, Wonderland.

Wonderland solution exists in multiple physical state spaces and acts as a global attractor.

Extension of no-hair theorem to $j$-form fields in anisotropic spaces.

Abstract

Why is the Universe so homogeneous and isotropic? We summarize a general study of a $\gamma$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a $j$-form (field-strength level), where $j\,\in\,\{1,3\}$, and the spaces studied are Bianchi space-times of solvable type. Wald's no-hair theorem is extended to include the $j$-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to exist in the physical state space of types I,II, IV, VI$_0$, VI$_h$, VII$_0$ and VII$_h$, and is a global attractor in I and V. The stability analysis of the other types has not yet been performed. This paper is a summary of ~[1], with some remarks towards new results which will be further laid out in upcoming work.