Combining Gravitational Wave Events with Galaxy Surveys to Infer the Hubble Constant

Abstract

The value of the Hubble constant quantifies the expansion rate of the universe, and is at the forefront of modern cosmology. Measurements from the Cosmic Microwave Background (CMB) by the Planck space telescope differ by approximately 5σ from measurements obtained from the cosmic distance ladder, which generally links geometry to Cepheid variable stars to type Ia supernovae. The discrepancy between these measurements (and others) is referred to as the Hubble tension. Gaining clarity on this tension will likely point to a greater understanding dark energy and possibly new physics. One promising method for resolving the tension is the introduction of gravitational wave cosmology, which offers a fundamentally new vantage point on the universe. Gravitational waves detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) have already been used as standard sirens to infer the Hubble constant, but do not currently have the number of events necessary weigh in with sufficient precision.

To maximize precision we will need to leverage the full catalog of gravitational wave events, not just the few bright sirens with identifiable electromagnetic counterparts. Most gravitational wave sources will have no identified electromagnetic counterpart, leading to uncertainty in the redshift of the source, and in turn a degeneracy between host galaxy distance, redshift, and H0. In these cases, it has been proposed that a statistical canvasing of candidate gravitational hosts, found in a large galaxy survey for example, can be used to accurately constrain the Hubble constant. We study and simulate this ``galaxy voting” method to compute H0. We find that the Hubble constant posterior is frequently biased relative to the true value even when making optimistic assumptions about the statistical properties of the sample. Using the MICECAT light-cone galaxy catalog, we find that the bias in the H0 posteriors depends on the realization of the underlying galaxy sample and the precision of the GW source distance measurement.

We also investigate the use of correlation functions as an alternative to the galaxy voting method. Using the same MICECAT simulated data, we compute the over-densities in the gravitational wave and galaxy populations as a function of luminosity distance and redshift, respectively. Correlating these two populations allows us to measure H0. We use the fast-Fourier transform code FFTLog to convert the real-space over-densities into weighted contributions to the angular power spectrum, from which we obtain radial constraints via tomography. We find forecasted H0 precision on the order of ∼ 20% in the two bin case when using gravitational wave number counts comparable to those used in current dark siren measurements of H0.