Non-Gaussianity from Self-Ordering Scalar Fields

TL;DR

This paper derives the bispectrum of density perturbations caused by self-ordered scalar fields, providing a new tool to detect these relics through their unique non-Gaussian signatures in cosmological data.

Contribution

It presents the first analytic expression for the bispectrum from self-ordered scalar fields, along with numerical evaluation and a simple approximation for data analysis.

Findings

The bispectrum peaks for aligned triangles, differing from local and equilateral models.

The non-Gaussianity could be detectable by Planck if the relic contribution is near current limits.

A compact analytic form of the bispectrum is provided for future cosmological analyses.

Abstract

The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges $k_1\simeq 2 k_2 \simeq 2 k_3$) as opposed to the local-model bispectrum, which peaks for squeezed triangles ($k_1\simeq k_2 \gg k_3$), and the equilateral bispectrum, which peaks at $k_1\simeq k_2 \simeq k_3$. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.