Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background

TL;DR

This paper develops a hierarchical Bayesian method and data analysis pipeline to detect early-universe relics like textures and bubble collisions in the CMB, applying it to WMAP data.

Contribution

It introduces an accurate approximation to the posterior distribution and a modular algorithm for robust detection and parameter estimation of localized sources in the CMB.

Findings

No evidence for textures or bubble collisions in WMAP data.

Constraints on the number of detectable sources: fewer than 4 bubble collisions and 5.2 textures at 95% confidence.

Enhanced detection sensitivity using adaptive-resolution techniques and optimal filters.

Abstract

A number of theoretically well-motivated additions to the standard cosmological model predict weak signatures in the form of spatially localized sources embedded in the cosmic microwave background (CMB) fluctuations. We present a hierarchical Bayesian statistical formalism and a complete data analysis pipeline for testing such scenarios. We derive an accurate approximation to the full posterior probability distribution over the parameters defining any theory that predicts sources embedded in the CMB, and perform an extensive set of tests in order to establish its validity. The approximation is implemented using a modular algorithm, designed to avoid a posteriori selection effects, which combines a candidate-detection stage with a full Bayesian model-selection and parameter-estimation analysis. We apply this pipeline to theories that predict cosmic textures and bubble collisions, extending previous analyses by using: (1) adaptive-resolution techniques, allowing us to probe features of arbitrary size, and (2) optimal filters, which provide the best possible sensitivity for detecting candidate signatures. We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to the standard cosmological model, and place robust constraints on the predicted number of such sources. The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively.