Clustering of Gravitational Wave and Supernovae events: a multitracer
  analysis in Luminosity Distance Space
  We study the clustering of Gravitational Wave (GW) merger events and
Supernovae IA (SN), as cosmic tracers in Luminosity Distance Space. We modify
the publicly available CAMB code to numerically evaluate auto- and cross- power
spectra for the different sources, including Luminosity Distance Space
distortion effects generated by peculiar velocities and lensing convergence. We
perform a multitracer Fisher analysis to forecast expected constraints on
cosmological and GW bias coefficients, using outputs from hydrodinamical N-body
simulations to determine the bias fiducial model and considering future
observations from the Vera Rubin Observatory and Einstein Telescope (ET), both
single and in a 3 detector network configuration. We find that adding SN to the
GW merger dataset considerably improves the forecast, mostly by breaking
significant parameter degeneracies, with final constraints comparable to those
obtainable from a Euclid-like survey. GW merger bias is forecasted to be
detectable with good significance even in the single ET case.
