Probing cosmic anisotropy with gravitational waves as standard sirens
  The gravitational wave (GW) as a standard siren directly determines the
luminosity distance from the gravitational waveform without reference to the
specific cosmological model, of which the redshift can be obtained separately
by means of the electromagnetic counterpart like GW events from binary neutron
stars and massive black hole binaries (MBHBs). To see to what extent the
standard siren can reproduce the presumed dipole anisotropy written in the
simulated data of standard siren events from typical configurations of GW
detectors, we find that (1) for the Laser Interferometer Space Antenna with
different MBHB models during five-year observations, the cosmic isotropy can be
ruled out at $3\sigma$ confidence level (C.L.) and the dipole direction can be
constrained roughly around $20\%$ at $2\sigma$ C.L., as long as the dipole
amplitude is larger than $0.03$, $0.06$ and $0.025$ for MBHB models Q3d, pop
III and Q3nod with increasing constraining ability, respectively; (2) for
Einstein Telescope with no less than $200$ standard siren events, the cosmic
isotropy can be ruled out at $3\sigma$ C.L. if the dipole amplitude is larger
than $0.06$, and the dipole direction can be constrained within $20\%$ at
$3\sigma$ C.L. if the dipole amplitude is near $0.1$; (3) for the Deci-Hertz
Interferometer Gravitational wave Observatory with no less than $100$ standard
siren events, the cosmic isotropy can be ruled out at $3\sigma$ C.L. for dipole
amplitude larger than $0.03$ , and the dipole direction can even be constrained
within $10\%$ at $3\sigma$ C.L. if the dipole amplitude is larger than $0.07$.
Our work manifests the promising perspective of the constraint ability on the
cosmic anisotropy from the standard siren approach.
