Possible use of self-calibration to reduce systematic uncertainties in determining distance-redshift relation via gravitational radiation from merging binaries

TL;DR

This paper proposes a self-calibration method using gravitational wave observations of merging binaries to improve the accuracy of the cosmic distance-redshift relation, reducing systematic uncertainties in future experiments.

Contribution

It introduces a novel iterative self-calibration technique leveraging optically identified sources to refine the distance-redshift relation in gravitational wave cosmology.

Findings

Analytical expression for achievable accuracy in self-calibration.

Lower limit on the number of sources needed for effective calibration.

Dependence of calibration limits on beam width and experimental parameters.

Abstract

By observing mergers of compact objects, future gravity wave experiments would measure the luminosity distance to a large number of sources to a high precision but not their redshifts. Given the directional sensitivity of an experiment, a fraction of such sources (gold plated -- GP) can be identified optically as single objects in the direction of the source. We show that if an approximate distance-redshift relation is known then it is possible to statistically resolve those sources that have multiple galaxies in the beam. We study the feasibility of using gold plated sources to iteratively resolve the unresolved sources, obtain the self-calibrated best possible distance-redshift relation and provide an analytical expression for the accuracy achievable. We derive lower limit on the total number of sources that is needed to achieve this accuracy through self-calibration. We show that this limit depends exponentially on the beam width and give estimates for various experimental parameters representative of future gravitational wave experiments DECIGO and BBO.