A Bayesian framework for cosmic string searches in CMB maps

Abstract

There exists various proposals to detect cosmic strings from Cosmic Microwave Background (CMB) or 21 cm temperature maps. Current proposals do not aim to find the location of strings on sky maps, all of these approaches can be thought of as a statistic on a sky map. We propose a Bayesian interpretation of cosmic string detection and within that framework, we derive a connection between estimates of cosmic string locations and cosmic string tension Gµ. We use this Bayesian framework to develop a machine learning framework for detecting strings from sky maps and outline how to implement this framework with neural networks. The neural network we trained was able to detect and locate cosmic strings on noiseless CMB temperature map down to a string tension of Gµ = 5 × 10 −9 and when analyzing a CMB temperature map that does not contain strings, the neural network gives a 0.95 probability that Gµ ≤ 2.3 × 10 −9 .

Information theoretic bounds on cosmic string detection in CMB maps with noise

“…Finally machine learning has been applied to the search for cosmic strings in CMB temperature maps (Ciuca & Hernández 2017;Vafaei Sadr et al 2018b;. These are the techniques that have achieved the best results so far.…”

“…The authors of Vafaei Sadr et al (2018b) used tree-based machine learning algorithms to place measurement limits of 1.2 × 10 −7 and 3.6×10 −9 for 0.9 arcmin resolution maps with noise and without noise, respectively. 1 The approach we took in Ciuca & Hernández (2017; was to develop and train a convolutional neural networks to estimate the locations of strings in a sky map. From the CNN estimates of string locations we inferred the string tension using Bayesian statistics.…”

“…Recently there has been a proliferation of methods (Hergt et al 2017;McEwen et al 2017;Vafaei Sadr et al 2018a;Ciuca & Hernández 2017 for the inference of the cosmic string tension Gµ from the Gott-Kaiser-Stebbings (GKS) effect (Gott 1985;Kaiser & Stebbins 1984) in cosmic microwave background (CMB) temperature anisotropy maps. In Ciuca & Hernández (2017; we argued for using convolutional neural networks (CNN) to find the locations of strings in the sky and then inferred the string tension using Bayesian statistics from those estimates. We found that in noiseless maps a measurement of G ∼ 10 −9 was possible.…”

A convolutional neural network for cosmic string detection in CMB temperature maps

“…They found more short edges in maps with strings which they interpreted as the disruption of long edges by Gaussian noise. However as shown in Ciuca & Hernández (2017) these edges do not necessarily correspond to the string locations. References Hergt et al (2017); McEwen et al (2017) used curvelet transforms to analyse simulated CMB temperature maps with noise, and most recently Vafaei Sadr et al (2018) has combined both Canny and curvelets to place a detection limit of Gµ ∼ 10 −7 on maps with realistic noise.…”

“…Furthermore none of the above proposals find the location of strings on sky maps. We recently proposed in Ciuca & Hernández (2017) a Bayesian interpretation of cosmic string detection and within that framework we improved on these shortcomings. First of all, our framework would allow different approaches, such as the ones described above, to be unified and studied systematically with machine learning used to search for the optimal combination of methods and choices within each approach.…”