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Register a new userPi from the sky -- A null test of general relativity from a population of gravitational wave observations
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Carl-Johan Haster
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Our understanding of observed Gravitational Waves (GWs) comes from matching data to known signal models describing General Relativity (GR). These models, expressed in the post-Newtonian formalism, contain the mathematical constant $pi$. Allowing $pi$ to vary thus enables a strong, universal and generalisable null test of GR. From a population of 22 GW observations, we make an astrophysical measurement of $pi=3.115^{+0.048}_{-0.088}$, and prefer GR as the correct theory of gravity with a Bayes factor of 321. We find the variable $pi$ test robust against simulated beyond-GR effects.
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Gravitational wave observations of compact binary coalescences provide precision probes of strong-field gravity. There is thus now a standard set of null tests of general relativity (GR) applied to LIGO-Virgo detections and many more such tests proposed. However, the relation between all these tests is not yet well understood. We start to investigate this by applying a set of standard tests to simulated observations of binary black holes in GR and with phenomenological deviations from GR. The phenomenological deviations include self-consistent modifications to the energy flux in an effective-one-body (EOB) model, the deviations used in the second post-Newtonian (2PN) TIGER and FTA parameterized tests, and the dispersive propagation due to a massive graviton. We consider four types of tests: residuals, inspiral-merger-ringdown consistency, parameterized (TIGER and FTA), and modified dispersion relation. We also check the consistency of the unmodeled reconstruction of the waveforms with the waveform recovered using GR templates. These tests are applied to simulated observations similar to GW150914 with both large and small deviations from GR and similar to GW170608 just with small deviations from GR. We find that while very large deviations from GR are picked up with high significance by almost all tests, more moderate deviations are picked up by only a few tests, and some deviations are not recognized as GR violations by any test at the moderate signal-to-noise ratios we consider. Moreover, the tests that identify various deviations with high significance are not necessarily the expected ones. We also find that the 2PN (1PN) TIGER and FTA tests recover much smaller deviations than the true values in the modified EOB (massive graviton) case. Additionally, we find that of the GR deviations we consider, the residuals test is only able to detect extreme deviations from GR. (Abridged)
Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of ${sim}2$; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of ${sim}2.6$ and bound the mass of the graviton to $m_g leq 1.76 times 10^{-23} mathrm{eV}/c^2$ with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to $delta hat{f}_{220} = 0.03^{+0.38}_{-0.35}$ for the fundamental quadrupolar mode, and $delta hat{f}_{221} = 0.04^{+0.27}_{-0.32}$ for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.
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.
Two new observational windows have been opened to strong gravitational physics: gravitational waves, and very long baseline interferometry. This suggests observational searches for new phenomena in this regime, and in particular for those necessary to make black hole evolution consistent with quantum mechanics. We describe possible features of compact quantum objects that replace classical black holes in a consistent quantum theory, and approaches to observational tests for these using gravitational waves. This is an example of a more general problem of finding consistent descriptions of deviations from general relativity, which can be tested via gravitational wave detection. Simple models for compact modifications to classical black holes are described via an effective stress tensor, possibly with an effective equation of state. A general discussion is given of possible observational signatures, and of their dependence on properties of the colliding objects. The possibility that departures from classical behavior are restricted to the near-horizon regime raises the question of whether these will be obscured in gravitational wave signals, due to their mutual interaction in a binary coalescence being deep in the mutual gravitational well. Numerical simulation with such simple models will be useful to clarify the sensitivity of gravitational wave observation to such highly compact departures from classical black holes.
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.
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