Gravitational Radiation, Inspiraling Binaries, and Cosmology

TL;DR

This paper demonstrates how gravitational wave observations of inspiraling binary systems can be used to measure key cosmological parameters like the Hubble constant and deceleration parameter, with realistic detection estimates.

Contribution

It provides a method to estimate cosmological parameters from gravitational wave data, including detection rates and measurement precision for LIGO-like detectors.

Findings

LIGO can observe approximately 50 inspiral events per year at certain thresholds.

About 100 observations can determine H_0 to 10% accuracy.

4000 years of observation are needed for 20% accuracy on q_0.

Abstract

We show how to measure cosmological parameters using observations of inspiraling binary neutron star or black hole systems in one or more gravitational wave detectors. To illustrate, we focus on the case of fixed mass binary systems observed in a single Laser Interferometer Gravitational-wave Observatory (LIGO)-like detector. Using realistic detector noise estimates, we characterize the rate of detections as a function of a threshold signal-to-noise ratio $\rho_0$, the Hubble constant $H_0$, and the binary ``chirp'' mass. For $\rho_0 = 8$, $H_0 = 100$ km/s/Mpc, and $1.4 \msun$ neutron star binaries, the sample has a median redshift of $0.22$. Under the same assumptions but independent of $H_0$, a conservative rate density of coalescing binaries ($8\times10^{-8}\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}$) implies LIGO will observe $\sim 50\,{\rm yr}^{-1}$ binary inspiral events. The precision with which $H_0$ and the deceleration parameter $q_0$ may be determined depends on the number of observed inspirals. For fixed mass binary systems, $\sim 100$ observations with $\rho_0 = 10$ in the LIGO detector will give $H_0$ to 10\% in an Einstein-DeSitter cosmology, and 3000 will give $q_0$ to 20\%. For the conservative rate density of coalescing binaries, 100 detections with $\rho_0 = 10$ will require about 4~yrs.