Cosmological Signatures of Anisotropic Spatial Curvature

TL;DR

This paper explores shear-free anisotropic cosmological models with curvature anisotropy, analyzing their effects on large-scale structure and CMB spectra, offering alternatives to isotropic inflationary models.

Contribution

It introduces shear-free models with anisotropic curvature, computes scalar perturbation correlations, and examines their impact on CMB observations as a novel alternative to standard isotropic cosmology.

Findings

Models are viable alternatives to isotropic inflation.

Anisotropic curvature affects the CMB spectrum.

Correlation functions are explicitly computed for these models.

Abstract

If one is willing to give up the cherished hypothesis of spatial isotropy, many interesting cosmological models can be developed beyond the simple anisotropically expanding scenarios. One interesting possibility is presented by shear-free models in which the anisotropy emerges at the level of the curvature of the homogeneous spatial sections, whereas the expansion is dictated by a single scale factor. We show that such models represent viable alternatives to describe the large-scale structure of the inflationary universe, leading to a kinematically equivalent Sachs-Wolfe effect. Through the definition of a complete set of spatial eigenfunctions we compute the two-point correlation function of scalar perturbations in these models. In addition, we show how such scenarios would modify the spectrum of the CMB assuming that the observations take place in a small patch of a universe with anisotropic curvature.