A framework for testing isotropy with the cosmic microwave background

TL;DR

This paper introduces a new framework for testing the Universe's isotropy using cosmic microwave background data, allowing constraints on scalar, vector, and tensor modes, and applies it to WMAP data with no evidence of anisotropy found.

Contribution

The paper develops a novel framework that constrains all degrees of freedom of anisotropy using Bianchi cosmologies and improves statistical analysis methods.

Findings

No evidence for anisotropy in WMAP data

Constraints on vector shear: < 1.7 x 10^-10 (95% CL)

Constraints on tensor shear: < 2.4 x 10^-7 (95% CL)

Abstract

We present a new framework for testing the isotropy of the Universe using cosmic microwave background data, building on the nested-sampling ANICOSMO code. Uniquely, we are able to constrain the scalar, vector and tensor degrees of freedom alike; previous studies only considered the vector mode (linked to vorticity). We employ Bianchi type VII$_h$ cosmologies to model the anisotropic Universe, from which other types may be obtained by taking suitable limits. In a separate development, we improve the statistical analysis by including the effect of Bianchi power in the high-$\ell$, as well as the low-$\ell$, likelihood. To understand the effect of all these changes, we apply our new techniques to WMAP data. We find no evidence for anisotropy, constraining shear in the vector mode to $(\sigma_V/H)_0 < 1.7 \times 10^{-10}$ (95% CL). For the first time, we place limits on the tensor mode; unlike other modes, the tensor shear can grow from a near-isotropic early Universe. The limit on this type of shear is $(\sigma_{T,\rm reg}/H)_0 < 2.4 \times 10^{-7}$ (95% CL).