Balancing Anisotropic Curvature with Gauge Fields in a Class of Shear-Free Cosmological Models

TL;DR

This paper classifies shear-free solutions in anisotropic, spatially homogeneous cosmologies with gauge fields, showing they can mimic standard FLRW models with an effective curvature influenced by gauge fields.

Contribution

It provides a complete list of shear-free solutions with multiple gauge fields in anisotropic cosmologies, extending understanding of gauge field effects on cosmic shear.

Findings

Solutions are dynamically equivalent to FLRW models with effective curvature.

Single gauge field solutions are limited to specific Bianchi types.

Multiple gauge fields allow additional shear-free solutions, including Bianchi type II.

Abstract

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of $n$ independent $p$-form gauge fields, where $p\in\{0,1,2,3\}$, in addition to standard $\Lambda$CDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant $K_{\rm{eff}}$ that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field ($n=1$) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI$_0$ and Kantowski-Sachs metric, which are dynamically equivalent to open ($K_{\rm{eff}}<0$), flat ($K_{\rm{eff}}=0$) and closed ($K_{\rm{eff}}>0$) FLRW models, respectively. With a collection of gauge fields ($n>1$) also Bianchi type II admits a shear-free solution ($K_{\rm{eff}}>0$). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.