The large scale structure in the 3D luminosity-distance space and its cosmological applications

Understand

Future gravitational wave (GW) observations are capable of detecting millions of compact star binary mergers in extragalactic galaxies, with $1\%$ luminosity-distance ($D_L$) measurement accuracy and better than arcminute positioning accuracy.

• This will open a new window of the large scale structure (LSS) of the universe, in the 3D {\bf luminosity-distance space (LDS)}, instead of the 3D redshift space of galaxy spectroscopic surveys.
• The baryon acoustic oscillation and the AP test encoded in the LDS LSS constrain the $D_L$-$D^{\rm co}_A$ (comoving angular diameter distance) relation and therefore the expansion history of the universe.
• Peculiar velocity induces the LDS distortion, analogous to the redshift space distortion, and allows for a new structure growth measure $f_L\sigma_8$.