Cosmological constraints on anisotropic Thurston geometries

TL;DR

This paper investigates anisotropic Thurston geometries as alternatives to the standard cosmological model, finding that their effects on the CMB are tightly constrained, requiring near-zero curvature to match observations.

Contribution

It introduces and analyzes a class of anisotropic homogeneous cosmological models based on Thurston geometries, deriving constraints from CMB observations.

Findings

CMB fluctuations are linked to curvature parameter $\

ext{Constraints require } | abla ext{Omega}_K| extless 10^{-5} ext{ for compatibility}

Anisotropic Thurston geometries are strongly limited by observational data.

Abstract

Much of modern cosmology relies on the Cosmological Principle, the assumption that the Universe is isotropic and homogeneous on sufficiently large scales, but it remains worthwhile to examine cosmological models that violate this principle slightly. We examine a class of such spacetimes that maintain homogeneity but break isotropy through their underlying local spatial geometries. These spacetimes are endowed with one of five anisotropic model geometries of Thurston's geometrization theorem, and their evolution is sourced with perfect fluid dust and cosmological constant. We show that the background evolution of these spacetimes induces fluctuations in the observed cosmic microwave background (CMB) temperature with amplitudes coupled to the curvature parameter $\Omega_K$. In order for these fluctuations to be compatible with the observed CMB angular power spectrum, we find $|\Omega_K| \lesssim 10^{-5}$ is required in all five geometries. This strongly limits the cosmological consequences of these models.