A Time Domain Waveform for Testing General Relativity

TL;DR

This paper proposes using corrected time domain waveforms to test General Relativity with gravitational waves, aiming to improve upon the stationary phase approximation by establishing a link between time and frequency domain models.

Contribution

It introduces a method to connect time domain waveforms with frequency domain models for testing GR, moving beyond the stationary phase approximation.

Findings

Preliminary MCMC results to assess eLISA's ability to detect deviations from GR.

Establishment of a phase-only correction framework in time domain waveforms.

Potential improvements in waveform modeling for gravitational wave tests of GR.

Abstract

Gravitational-wave parameter estimation is only as good as the theory the waveform generation models are based upon. It is therefore crucial to test General Relativity (GR) once data becomes available. Many previous works, such as studies connected with the ppE framework by Yunes and Pretorius, rely on the stationary phase approximation (SPA) to model deviations from GR in the frequency domain. As Fast Fourier Transform algorithms have become considerably faster and in order to circumvent possible problems with the SPA, we test GR with corrected time domain waveforms instead of SPA waveforms. Since a considerable amount of work has been done already in the field using SPA waveforms, we establish a connection between leading-order-corrected waveforms in time and frequency domain, concentrating on phase-only corrected terms. In a Markov Chain Monte Carlo study, whose results are preliminary and will only be available later, we will assess the ability of the eLISA detector to measure deviations from GR for signals coming from supermassive black hole inspirals using these corrected waveforms.