Exploring the distance-redshift relation with gravitational wave standard sirens and tomographic weak lensing

TL;DR

This paper proposes using cross-correlations between gravitational wave standard sirens and tomographic weak lensing to precisely measure cosmological parameters, including the Hubble constant, with upcoming surveys.

Contribution

It introduces a novel method combining standard sirens and weak lensing auto- and cross-correlations to constrain cosmological parameters.

Findings

Potential to tightly constrain the Hubble parameter with 0.33 km/s/Mpc accuracy.

Demonstrates the effectiveness of cross-correlation techniques with Euclid and Einstein Telescope data.

Shows promise for probing the distance scale in cosmology.

Abstract

Gravitational waves from inspiraling compact objects provide us with information of the distance scale since we can infer the absolute luminosity of the source from analysis of the wave form, which is known as standard sirens. The first detection of the gravitational wave signal of the binary black hole merger event by Advanced LIGO has opened up the possibility of utilizing standard sirens as cosmological probe. In order to extract information of the distance-redshift relation, we cross-correlate weak lensing, which is an unbiased tracer of matter distribution in the Universe, with the projected number density of gravitational wave sources. For weak lensing, we employ tomography technique to efficiently obtain information of large-scale structures at wide ranges of redshifts. Making use of the cross-correlations along with the auto-correlations, we present forecast of constraints on four cosmological parameters, i.e., Hubble parameter, matter density, the equation of state parameter of dark energy, and the amplitude of matter fluctuation. To fully explore the ability of cross-correlations, which require large overlapping sky coverage, we consider the specific case with the upcoming surveys by \textit{Euclid} for weak lensing and Einstein Telescope for standard sirens. We show that cosmological parameters can be tightly constrained solely by these auto- and cross-correlations of standard sirens and weak lensing. For example, the $1\text{-}\sigma$ error of Hubble parameter is expected to be $\sigma (H_0) = 0.33 \, \mathrm{km} \, \mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$. Thus, the proposed statistics will be a promising probe into the distance scale.