Information Theoretic Bounds on Cosmic String Detection in CMB Maps with Noise

TL;DR

This paper derives information theoretic bounds on the detectability of cosmic string tensions in CMB maps, considering noise and resolution, and evaluates these bounds for upcoming experiments, highlighting fundamental detection limits.

Contribution

It introduces an information theoretic framework to bound cosmic string detection in CMB data, accounting for noise and resolution, and assesses the limits for major CMB experiments.

Findings

Detection of string tensions below 10^{-7} is limited by noise.

Information bounds cannot be saturated by any detection method.

Bounds are evaluated for ACT, SPT-3G, Simons Observatory, CMB-S4.

Abstract

We use a convolutional neural network (CNN) to study cosmic string detection in cosmic microwave background (CMB) flat sky maps with Nambu-Goto strings. On noiseless maps we can measure string tensions down to order $10^{-9}$, however when noise is included we are unable to measure string tensions below $10^{-7}$. Motivated by this impasse, we derive an information theoretic bound on the detection of the cosmic string tension $G\mu$ from CMB maps. In particular we bound the information entropy of the posterior distribution of $G\mu$ in terms of the resolution, noise level and total survey area of the CMB map. We evaluate these bounds for the ACT, SPT-3G, Simons Observatory, Cosmic Origins Explorer, and CMB-S4 experiments. These bounds cannot be saturated by any method.