  Many recent works have shown that the angular resolution of ground-based
detectors is too poor to characterize the anisotropies of the stochastic
gravitational-wave background (SGWB). For this reason, we asked ourselves if a
constellation of space-based instruments could be more suitable. We consider
the Laser Interferometer Space Antenna (LISA), a constellation of multiple
LISA-like clusters, and the Deci-hertz Interferometer Gravitational-wave
Observatory (DECIGO). Specifically, we test whether these detector
constellations can probe the anisotropies of the SGWB. For this scope, we
considered the SGWB produced by two astrophysical sources: merging compact
binaries and a recently proposed scenario for massive black-hole seed formation
through multiple mergers of stellar remnants. We find that measuring the
angular power spectrum of the SGWB anisotropies is almost unattainable.
However, it turns out that it could be possible to probe the SGWB anisotropies
through cross-correlation with the CMB fluctuations. In particular, we find
that a constellation of two LISA-like detectors and CMB-S4 can marginally
constrain the cross-correlation between the CMB lensing convergence and the
SGWB produced by the black hole seed formation process. Moreover, we find that
DECIGO can probe the cross-correlation between the CMB lensing and the SGWB
from merging compact binaries.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics