Do Cosmological Perturbations Have Zero Mean?

TL;DR

This paper tests whether cosmological perturbations truly have zero mean, using a model-independent statistical approach on WMAP data, and finds no significant evidence for a non-zero mean after correction for multiple testing.

Contribution

It introduces a generic, model-independent test for the zero mean hypothesis of cosmological perturbations using CMB data.

Findings

Evidence for non-zero mean in some multipoles before correction.

No significant non-zero mean after multiple testing correction.

Constraints on mean temperature multipoles as a function of angular scale.

Abstract

A central assumption in our analysis of cosmic structure is that cosmological perturbations have zero ensemble mean. This property is one of the consequences of statistically homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which perturbations have non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and is thus rather generic and model-independent. The test statistic we employ is essentially Student's t statistic, applied to appropriately masked, foreground-cleaned cosmic microwave background anisotropy maps produced by the WMAP mission. We find evidence for a non-zero mean in a particular range of multipoles, but the evidence against the zero mean hypothesis goes away when we correct for multiple testing. We also place constraints on the mean of the temperature multipoles as a function of angular scale. On angular scales smaller than four degrees, a non-zero mean has to be at least an order of magnitude smaller than the standard deviation of the temperature anisotropies.