Probing Primordial Stochastic Gravitational Wave Background with Multi-band Astrophysical Foreground Cleaning

The primordial stochastic gravitational wave background (SGWB) carries first-hand messages of early-universe physics, possibly including effects from inflation, preheating, cosmic strings, electroweak symmetry breaking, and etc. However, the astrophysical foreground from compact binaries may mask the SGWB, introducing difficulties in detecting the signal and measuring it accurately. In this paper, we propose a foreground cleaning method taking advantage of gravitational wave observations in other frequency bands. We apply this method to probing the SGWB with space-borne gravitational wave detectors, such as the laser interferometer space antenna (LISA). We find that the spectral density of the LISA-band astrophysical foreground from compact binaries (black holes and neutron stars) can be predicted with percent-level accuracy assuming 10-years' observations of third-generation GW detectors, e.g., cosmic explorer. While this multi-band method does not apply to binary white dwarfs (BWDs) which usually merger before entering the frequency band of ground-based detectors, we limit our foreground cleaning to frequency higher than $\sim5$ mHz, where all galactic BWDs can be individually resolved by LISA and the shape of the spectral density of the foreground from extragalactic BWDs can be reconstructed and/or modeled with certain uncertainties. After the foreground cleaning, LISA's sensitivity to the primordial SGWB will be substantially improved for either two LISA constellations where SGWB can be measured by cross correlating their outputs or only one constellation with three spacecrafts where SGWB can be measured by contrasting the responses of a signal channel and a null channel.