Supermassive Black Hole Tests of General Relativity with eLISA

TL;DR

This paper investigates the ability of eLISA to test general relativity using gravitational wave signals from supermassive black hole binaries, focusing on phase corrections predicted by alternative gravity theories and their detectability.

Contribution

It develops analytical time domain waveforms incorporating phase corrections from alternative theories and assesses their detectability and parameter estimation capabilities with eLISA.

Findings

GR waveforms suffice for higher PN order corrections

Non-GR waveforms needed for low PN order corrections

eLISA can test certain deviations from GR in black hole mergers

Abstract

Motivated by the parameterized post-Einsteinian (ppE) scheme devised by Yunes and Pretorius, which introduces corrections to the post-Newtonian coefficients of the frequency domain gravitational waveform in order to emulate alternative theories of gravity, we compute analytical time domain waveforms that, after a numerical Fourier transform, aim to represent (phase corrected only) ppE waveforms. In this formalism, alternative theories manifest themselves via corrections to the phase and frequency, as predicted by General Relativity (GR), at different post-Newtonian (PN) orders. In order to present a generic test of alternative theories of gravity, we assume that the coupling constant of each alternative theory is manifestly positive, allowing corrections to the GR waveforms to be either positive or negative. By exploring the capabilities of massive black hole binary GR waveforms in the detection and parameter estimation of corrected time domain ppE signals, using the current eLISA configuration (as presented for the ESA Cosmic Vision L3 mission), we demonstrate that for corrections arising at higher than 1PN order in phase and frequency, GR waveforms are sufficient for both detecting and estimating the parameters of alternative theory signals. However, for theories introducing corrections at the 0 and 0.5 PN order, GR waveforms are not capable of covering the entire parameter space, requiring the use of non-GR waveforms for detection and parameter estimation.