Two-point Correlation Functions in Inhomogeneous and Anisotropic Cosmologies

TL;DR

This paper introduces a new formalism based on isometries to determine two-point correlation functions in inhomogeneous and anisotropic cosmologies, simplifying analysis without full perturbation theory.

Contribution

The paper presents a novel method leveraging background isometries to directly fix correlation function dependence, applicable to various cosmological models.

Findings

Constructed CMB temperature correlation functions for inhomogeneous and anisotropic universes.

Derived covariance matrices in near-Friedmannian limits.

Extended the method to three-point correlation functions in simple geometries.

Abstract

Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance arguments can be used to fix the functional dependence of this function as the invariant distance between any two points. In this paper we introduce a novel formalism which fixes this functional dependence directly from the isometries of the background metric, thus allowing one to quickly assess the overall features of Gaussian correlators without resorting to the full machinery of perturbation theory. As an application we construct the CMB temperature correlation function in one inhomogeneous (namely, an off-center LTB model) and two spatially flat and anisotropic (Bianchi) universes, and derive their covariance matrices in the limit of almost Friedmannian symmetry. We show how the method can be extended to arbitrary N -point correlation functions and illustrate its use by constructing three-point correlation functions in some simple geometries.