Tensor Perturbations in Anisotropically Curved Cosmologies

TL;DR

This paper investigates tensor perturbations in cosmologies with anisotropic spatial curvature, revealing unique behaviors of tensor modes and providing analytical solutions relevant for future CMB polarization constraints.

Contribution

It derives the linear dynamics of tensor perturbations in anisotropically curved cosmologies, highlighting differences from isotropic cases and emphasizing the coupling with scalar and vector modes.

Findings

Tensor polarizations behave as spin-0 and spin-1 components.

Analytical solutions for tensor modes in radiation-dominated universe.

Potential constraints from future CMB polarization experiments.

Abstract

Besides expanding anisotropically, the universe can also be anisotropic at the level of its (spatial) curvature. In particular, models with anisotropic curvature and isotropic expansion leads both to a $\Lambda$CDM-like phenomenology and to an isotropic and homogeneous CMB at the background level. Thus, they offer an interesting and viable example where the cosmological principle does not follow from the isotropy of observational data. In this paper we extract the linear dynamics of tensor perturbations in two classes of cosmologies with anisotropic spatial curvature. Two difficulties arise in comparison to the same computation in isotropic cosmologies. First, the two tensor polarizations do not behave as a spin-2 field, but rather as the spin-0 and spin-1 irreducible components of a symmetric, traceless and transverse tensor field, each with its own dynamics. Second, because metric perturbations are algebraically coupled, one cannot ignore scalar and vector modes and focus just on tensors --- even if one is only interested in the latter --- under the penalty of obtaining the wrong equations of motion. We illustrate our results by finding analytical solutions and evaluating the power-spectra of tensor polarizations in a radiation dominated universe. We conclude with some comments on how these models could be constrained with future experiments on CMB polarization.