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The cosmological principle has been verified using electromagnetic (EM)observations. However its verification with high accuracy is challenging due tovarious foregrounds and selection effects, and possible violation of thecosmological principle has been reported in the literature. In contrast,gravitational wave (GW) observations are free of these foregrounds and relatedselection biases. This may enable future GW experiments to test thecosmological principle robustly with full sky distribution of millions ofstandard bright/dark sirens. However, the sensitivities of GW detectors arehighly anisotropic, resulting in significant instrument induced anisotropies inthe observed GW catalog. We investigate these instrumental effects for 3rdgeneration detector networks in term of multipoles $a_{\ell m}$ of the observedGW source distribution, using Monte Carlo simulations. (1) We find that theinstrument induced anisotropy primarily exists at the $m=0$ modes on largescales ($\ell \lesssim 10$), with amplitude $\langle |a_{\ell 0}|^2 \rangle\sim 10^{-3}$ for two detectors (ET-CE) and $\sim 10^{-4}$ for three detectors(ET-2CE). This anisotropy is correlated with the sky distribution ofsignal-to-noise ratio (SNR) and localization accuracy. Such anisotropy sets alower limit on the detectable cosmological $a_{\ell 0}$. (2) However, we findthat the instrument induced anisotropy is efficiently canceled by rotation ofthe Earth in $m\neq 0$ components of $a_{\ell m}$. Therefore $a_{\ell m}$($m\neq 0$) are clean windows to detect cosmological anisotropies. (3) Weinvestigate the capability of 3rd generation GW experiments to measure thecosmic dipole. Through Monte Carlo simulations, we find that cosmic dipole withan amplitude of $\sim 10^{-2}$ reported in the literature can be detected/ruledout by ET-CE and ET-2CE robustly, through the measurement of $a_{11}$.

Detector induced anisotropies on the angular distribution of gravitational wave sources and opportunities of constraining horizon scale anisotropies