Can we use Next-Generation Gravitational Wave Detectors for Precision Measurements of Shapiro Delay?

Abstract

Shapiro time delay is one of the fundamental tests of general relativity. To date all measurements of time delay have been conducted on astronomical scales. It was asserted in 2010 that gravitational wave detectors on Earth could be used to measure Shapiro delay on a terrestrial scale via massive rotating systems. Building on that work, we consider how measurements of Shapiro delay can be made using next-generation gravitational wave detectors. We perform an analysis for measuring Shapiro delay with the next-generation gravitational wave detector Cosmic Explorer to determine how precisely the effect can be measured. Using a rotating mass unit design, we find that Cosmic Explorer can measure the Shapiro delay signal with an amplitude signal to noise ratio (SNR) up to \(\sim37\) in 1 year of integration time. By measuring Shapiro delay with this technique, Cosmic Explorer will allow for terrestrial measurements of \(\gamma\) in the paramaterized post-Newtonian formalism of gravity with precision of \(<1\%\).