Number count of Gravitational Waves and Supernovae in Luminosity Distance space for LCDM and Scalar-Tensor theories

TL;DR

This paper derives the full relativistic expression for gravitational wave and supernovae counts in luminosity distance space within LCDM and scalar-tensor theories, assessing their detectability and cosmological implications.

Contribution

It provides the first comprehensive derivation of relativistic corrections for gravitational wave counts in luminosity distance space, including comparisons with supernovae and galaxy counts.

Findings

Relativistic effects significantly impact gravitational wave counts.

Detectability of signals varies with current and future GW detectors.

Relativistic corrections offer insights into the growth of structure and gravity theories.

Abstract

The clustering of gravitational waves in luminosity distance space is emerging as a promising probe of the growth of structure. Just like for galaxies, its osbervation is subject to a number of relativistic corrections that affect the measured signal and need to be accounted for when fitting theoretical models to the data. We derive the full expression for the number count of gravitational waves in luminosity distance space, including all relativistic corrections, in LCDM and in scalar-tensor theories with luminal propagation of tensors. We investigate the importance of each relativistic effect and the detectability of the total signal by current and planned GW detectors. We consider also supernovae in luminosity distance space, highlighting the differences with gravitational waves in the case of scalar-tensor theories. We carry out a thorough comparison among the number count of gravitational waves and supernovae in luminosity distance space, and that of galaxies in redshift space. We show how the relativistic corrections contain useful complementary information on the growth of perturbations and on the underlying theory of gravity, highlighting the synergy with other cosmological probes.