Tests of General Relativity and Alternative theories of gravity using Gravitational Wave observations

TL;DR

This paper reviews methods for testing General Relativity and alternative gravity theories using gravitational wave data, comparing model-dependent and model-independent approaches, and discusses the potential of space-based detectors like eLISA.

Contribution

It provides a comprehensive comparison of bounds on gravity theories from different detectors and extends SVD-based analysis to space-based GW observations.

Findings

Space-based detectors can test gravity theories with unprecedented accuracy.

SVD of Fisher matrix improves Post-Newtonian tests.

eLISA can place competitive bounds on alternative theories.

Abstract

Gravitational Wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test General Relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories like Scalar-Tensor theories, Dynamical Chern-Simons theory and Massive graviton theories. Model independent tests are attempts to write down a parametrised gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA configuration. We also compare the expected bounds on alternative theories of gravity from ground-based and space-based detectors and find that space-based GW detectors can test GR and other theories of gravity with unprecedented accuracies. We then focus on a recent proposal to use singular value decomposition (SVD) of the Fisher information matrix to improve the accuracies with which Post-Newtonian (PN) theory can be tested. We extend those results to the case of space based detector eLISA and discuss its implications.