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Register a new userTesting general relativity with gravitational-wave catalogs: the insidious nature of waveform systematics
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Gravitational-wave observations of binary black holes allow new tests of general relativity to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal, otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with general relativity. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more stringent tests of gravity by analyzing large numbers of events together. However, there is a danger that waveform errors can accumulate among events: even if the waveform model is accurate enough for each individual event, it can still yield erroneous evidence for new physics when applied to a large catalog. This paper presents a simple linearised analysis, in the style of a Fisher matrix calculation, that reveals the conditions under which the apparent evidence for new physics due to waveform errors grows as the catalog size increases. We estimate that, in the worst-case scenario, evidence for a deviation from general relativity might appear in some tests using a catalog containing as few as 10-30 events above a signal-to-noise ratio of 20. This is close to the size of current catalogs and highlights the need for caution when performing these sorts of experiments.
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Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurate tests of gravity with gravitational waves.
Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study strong field, dynamical gravity. Extracting detailed information about these systems requires accurate theoretical models of the gravitational wave signals. If gravity is not described by General Relativity, analyses that are based on waveforms derived from Einsteins field equations could result in parameter biases and a loss of detection efficiency. A new class of parameterized post-Einsteinian (ppE) waveforms has been proposed to cover this eventuality. Here we apply the ppE approach to simulated data from a network of advanced ground based interferometers (aLIGO/aVirgo) and from a future spaced based interferometer (LISA). Bayesian inference and model selection are used to investigate parameter biases, and to determine the level at which departures from general relativity can be detected. We find that in some cases the parameter biases from assuming the wrong theory can be severe. We also find that gravitational wave observations will beat the existing bounds on deviations from general relativity derived from the orbital decay of binary pulsars by a large margin across a wide swath of parameter space.
Gravitational-wave (GW) observations by a network of ground-based laser interferometric detectors allow us to probe the nature of GW polarizations. This would be an interesting test of general relativity (GR), since GR predicts only two polarization modes while there are theories of gravity that predict up to six polarization modes. The ability of GW observations to probe the nature of polarizations is limited by the available number of linearly independent detectors in the network. (To extract all polarization modes, there should be at least as many detectors as the polarization modes.) Strong gravitational lensing of GWs offers a possibility to significantly increase the effective number of detectors in the network. Due to strong lensing (e.g., by galaxies), multiple copies of the same signal can be observed with time delays of several minutes to weeks. Owing to the rotation of the earth, observation of the multiple copies of the same GW signal would allow the network to measure different combinations of the same polarizations. This effectively multiplies the number of detectors in the network. Focusing on strongly lensed signals from binary black hole mergers that produce two observable images, using Bayesian model selection and assuming simple polarization models, we show that our ability to distinguish between polarization models is significantly improved.
The direct detection of gravitational waves with upcoming second-generation gravitational wave detectors such as Advanced LIGO and Virgo will allow us to probe the genuinely strong-field dynamics of general relativity (GR) for the first time. We present a data analysis pipeline called TIGER (Test Infrastructure for GEneral Relativity), which is designed to utilize detections of compact binary coalescences to test GR in this regime. TIGER is a model-independent test of GR itself, in that it is not necessary to compare with any specific alternative theory. It performs Bayesian inference on two hypotheses: the GR hypothesis $mathcal{H}_{rm GR}$, and $mathcal{H}_{rm modGR}$, which states that one or more of the post-Newtonian coefficients in the waveform are not as predicted by GR. By the use of multiple sub-hypotheses of $mathcal{H}_{rm modGR}$, in each of which a different number of parameterized deformations of the GR phase are allowed, an arbitrarily large number of testing parameters can be used without having to worry about a model being insufficiently parsimonious if the true number of extra parameters is in fact small. TIGER is well-suited to the regime where most sources have low signal-to-noise ratios, again through the use of these sub-hypotheses. Information from multiple sources can trivially be combined, leading to a stronger test. We focus on binary neutron star coalescences, for which sufficiently accurate waveform models are available that can be generated fast enough on a computer to be fit for use in Bayesian inference. We show that the pipeline is robust against a number of fundamental, astrophysical, and instrumental effects, such as differences between waveform approximants, a limited number of post-Newtonian phase contributions being known, the effects of neutron star spins and tidal deformability on the orbital motion, and instrumental calibration errors.
One century after its formulation, Einsteins general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.
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