The observed number counts in luminosity distance space
Abstract
Next generation surveys will provide us with an unprecedented number of detections of supernovae Type Ia and gravitational wave merger events. Crosscorrelations of such objects offer novel and powerful insights into the largescale distribution of matter in the universe. Both of these sources carry information on their luminosity distance, but remain uninformative about their redshifts; hence their clustering analyses and crosscorrelations need to be carried out in luminosity distance space, as opposed to redshift space. In this paper, we calculate the full expression for the number count fluctuation in terms of a perturbation to the observed luminosity distance. We find the expression to differ significantly from the one commonly used in redshift space. Furthermore, we present a comparison of the number count angular power spectra between luminosity distance and redshift spaces. We see a wide divergence between the two at large scales, and we note that lensing is the main contribution to such differences. On such scales and at higher redshifts the difference between the angular power spectra in luminosity distance and redshift spaces can be roughly 50%. We also investigate crosscorrelating different redshift bins using different tracers, i.e. one in luminosity distance space and one in redshift, simulating the crosscorrelation angular power spectrum between background gravitational waves/supernovae and foreground galaxies. Finally, we show that in a cosmic variance limited survey, the relativistic corrections to the densityonly term ought to be included.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 August 2023
 DOI:
 10.1088/14757516/2023/08/050
 arXiv:
 arXiv:2304.14253
 Bibcode:
 2023JCAP...08..050F
 Keywords:

 galaxy clustering;
 galaxy clusters;
 gravitational waves / theory;
 supernova type Ia  standard candles;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 34 pages, 9 figures, 1 table. Agrees with published version