Astrometric Effects of Gravitational Wave Backgrounds with non-Luminal Propagation Speeds

TL;DR

This paper explores how gravitational wave backgrounds with different propagation speeds affect astrometric measurements, providing methods to constrain gravity's speed through observed stellar position shifts.

Contribution

It introduces a framework to analyze astrometric effects of gravitational waves with non-luminal speeds, including correlation functions and power spectra, to test gravity theories.

Findings

Sub-luminal gravitational waves enhance low-order angular modes.

Super-luminal gravitational waves suppress low-order angular modes.

Analytical models for redshift and astrometry correlations are developed.

Abstract

A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would result in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed.