Measuring the primordial gravitational wave background in the presence of other stochastic signals

TL;DR

This paper develops a generalized method for extracting the primordial gravitational wave background from interferometric data, accounting for foreground signals and enabling more accurate detection with missions like LISA.

Contribution

It introduces a formalism for optimal filtering and SNR calculation that marginalizes over foreground signals, improving SGWB extraction techniques.

Findings

Derived expressions for optimal filter and SNR in complex backgrounds

Generalized methodology to template-free reconstruction of SGWB

Demonstrated application with LISA mission data

Abstract

Standard methodologies for the extraction of the stochastic gravitational wave background (SGWB) from auto- or cross-correlation of interferometric signals often involve the use of a filter function. The standard optimal filter maximizes the signal-to-noise ratio (SNR) between the total SGWB and the noise. We derive expressions for the optimal filter and SNR in the presence of a target SGWB plus other unwanted components. We also generalize the methodology to the case of template-free reconstruction. The formalism allows to easily perform analyses and forecasts that marginalize over foreground signals, such as the typical $\Omega_{\rm GW} \propto f^{2/3}$ background arising from binary coalescence. We demonstrate the methodology with the LISA mission and discuss possible extensions and domains of application.