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.
