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

Abstract

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 $D_L$-$D_A^{\mathrm{co}}$ (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 $f_L{\sigma }_8$. When the distance duality is enforced ($1+z=D_L/D_A^{\mathrm{co}}$), the LDS LSS by itself determines the redshift to $\sim 1\%$ level accuracy, and alleviates the need of spectroscopic follow-up of GW events.But a more valuable application is to test the distance duality to $1\%$ level accuracy, in combination with conventional BAO and supernovae measurements. This will put stringent constraints on modified gravity models in which the gravitational wave $D_L^{\mathrm{GW}}$ deviates from the electromagnetic wave $D_L^{EM}$. All these applications require no spectroscopic follow-ups.

arXiv comment5 pages, to be submitted to PRL

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