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

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(GW) proportional to f(2/3) background arising from binary coalescence. We demonstrate the methodology with the LISA mission and discuss possible extensions and domains of application.

Automated summary

This study focuses on the standard methodologies for extracting SGWB from interferometric signals, involving the use of filter functions to maximize SNR. It derives expressions for optimal filter and SNR in the presence of target SGWB and other unwanted components, and generalizes the methodology to template-free reconstruction. The formalism allows for easy analysis and forecasting while marginalizing foreground signals.