  Identifying the anisotropies in a cosmologically sourced stochastic
gravitational wave background (SGWB) would be of significance in shedding light
on the nature of primordial inhomogeneities. For example, if SGWB carries
isocurvature fluctuations, it would provide evidence for a multi-field
inflationary origin of these inhomogeneities. However, this is challenging in
practice due to finite detector sensitivity and also the presence of the
astrophysical foregrounds that can compete with the cosmological signal. In
this work, we explore the prospects for measuring cosmological SGWB
anisotropies in the presence of an astrophysical counterpart and detector
noise. To illustrate the main idea, we perform a Fisher analysis using a
well-motivated cosmological SGWB template corresponding to a first order phase
transition, and an astrophysical SGWB template corresponding to extra-galactic
binary mergers, and compute the uncertainty with which various parameters
characterizing the isotropic and anisotropic components can be extracted. We
also discuss some subtleties and caveats involving shot noise in the
astrophysical foreground. Overall, we show that upcoming experiments, e.g.,
LISA, Taiji, Einstein Telescope, Cosmic Explorer, and BBO, can all be effective
in discovering plausible anisotropic cosmological SGWBs.
