Certain scalar-tensor theories have the property of endowing stars with scalar hair, sourced either by the stars own compactness (spontaneous scalarization) or, for binary systems, by the companions scalar hair (induced scalarization) or by the orbital binding energy (dynamical scalarization). Scalarized stars in binaries present different conservative dynamics than in General Relativity, and can also excite a scalar mode in the metric perturbation that carries away dipolar radiation. As a result, the binary orbit shrinks faster than predicted in General Relativity, modifying the rate of decay of the orbital period. In spite of this, scalar-tensor theories can pass existing binary pulsar tests, because observed pulsars may not be compact enough or sufficiently orbitally bound to activate scalarization. Gravitational waves emitted during the last stages of compact binary inspirals are thus ideal probes of scalarization effects. For the standard projected sensitivity of advanced LIGO, we here show that, if neutron stars are sufficiently compact to enter the detectors sensitivity band already scalarized, then gravitational waves could place constraints at least comparable to binary pulsars. If the stars dynamically scalarize while inspiraling in band, then constraints are still possible provided the scalarization occurs sufficiently early in the inspiral, roughly below an orbital frequency of 50Hz. In performing these studies, we derive an easy-to-calculate data analysis measure, an integrated phase difference between a General Relativistic and a modified signal, that maps directly to the Bayes factor so as to determine whether a modified gravity effect is detectable. Finally, we find that custom-made templates are equally effective as model-independent, parameterized post-Einsteinian waveforms at detecting such modified gravity effects at realistic signal-to-noise ratios.
Waveform templates are a powerful tool for extracting and characterizing gravitational wave signals, acting as highly restrictive priors on the signal morphologies that allow us to extract weak events buried deep in the instrumental noise. The templates map the waveform shapes to physical parameters, thus allowing us to produce posterior probability distributions for these parameters. However, there are attendant dangers in using highly restrictive signal priors. If strong field gravity is not accurately described by General Relativity (GR), then using GR templates may result in fundamental bias in the recovered parameters, or even worse, a complete failure to detect signals. Here we study such dangers, concentrating on three distinct possibilities. First, we show that there exist modified theories compatible with all existing tests that would fail to be detected by the LIGO/Virgo network using searches based on GR templates, but which would be detected using a one parameter post-Einsteinian extension. Second, we study modified theories that produce departures from GR that turn on suddenly at a critical frequency, producing waveforms that do not naively fit into the simplest parameterized post-Einsteinian (ppE) scheme. We show that even the simplest ppE templates are still capable of picking up these strange signals and diagnosing a departure from GR. Third, we study whether using inspiral-only ppE waveforms for signals that include merger and ringdown can lead to problems in misidentifying a GR departure. We present an easy technique that allows us to self-consistently identify the inspiral portion of the signal, and thus remove these potential biases, allowing GR tests to be performed on higher mass signals that merge within the detector band. We close by studying a parameterized waveform model that may allow us to test GR using the full inspiral-merger-ringdown signal.
We study generic tests of strong-field General Relativity using gravitational waves emitted during the inspiral of compact binaries. Previous studies have considered simple extensions to the standard post-Newtonian waveforms that differ by a single term in the phase. Here we improve on these studies by (i) increasing the realism of injections and (ii) determining the optimal waveform families for detecting and characterizing such signals. We construct waveforms that deviate from those in General Relativity through a series of post-Newtonian terms, and find that these higher-order terms can affect our ability to test General Relativity, in some cases by making it easier to detect a deviation, and in some cases by making it more difficult. We find that simple single-phase post-Einsteinian waveforms are sufficient for detecting deviations from General Relativity, and there is little to be gained from using more complicated models with multiple phase terms. The results found here will help guide future attempts to test General Relativity with advanced ground-based detectors.
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.
