CMB Temperature Polarization Correlation and Primordial Gravitational Waves II: Wiener Filtering and Tests Based on Monte Carlo Simulations

TL;DR

This paper explores Wiener filtering of CMB TE data to isolate primordial gravitational wave signals, comparing various statistical tests and methods to optimize detection prospects in ideal and realistic experimental scenarios.

Contribution

It introduces a Wiener filtering approach to enhance PGW detection in CMB TE data and compares multiple statistical tests and methods for their effectiveness.

Findings

Ideal experiment can detect r=0.3 at 98% confidence with S/N test

Zero multipole method outperforms other tests in realistic conditions

Detection sensitivity depends heavily on experimental noise levels

Abstract

In this paper we continue our study of CMB TE cross correlation as a source of information about primordial gravitational waves. In an accompanying paper, we considered the zero multipole method. In this paper we use Wiener filtering of the CMB TE data to remove the density perturbation contribution to the TE power spectrum. In principle this leaves only the contribution of PGWs. We examine two toy experiments (one ideal and one more realistic), to see how well they constrain PGWs using the TE power spectrum. We consider three tests applied to a combination of observational data and data sets generated by Monte Carlo simulations: (1) Signal-to-Noise test, (2) sign test, and (3) Wilcoxon rank sum test. We compare these tests with each other and with the zero multipole method. Finally, we compare the signal-to-noise ratio of TE correlation measurements first with corresponding signal-to-noise ratios for BB ground based measurements and later with current and future TE correlation space measurements. We found that an ideal TE correlation experiment limited only by cosmic variance can detect PGWs with a tensor-to-scalar ratio $r=0.3$ at 98% confidence level with the $S/N$ test, 93% confidence level with the sign test, and 80% confidence level for the Wilcoxon rank sum test. We also compare all results with corresponding results obtained using the zero multipole method. We demonstrate that to measure PGWs by their contribution to the TE cross correlation power spectrum in a realistic ground based experiment when real instrumental noise is taken into account, the tensor-to-scalar ratio, $r$, must be approximately four times larger. In the sense to detect PGWs, the zero multipole method is the best, next best is the S/N test, then the sign test, and the worst is the Wilcoxon rank sum test.