Laura Sampson

Gravitational Wave Tests of General Relativity with the Parameterized Post-Einsteinian Framework

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.

Projected Constraints on Scalarization with Gravitational Waves from Neutron Star Binaries

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.

Gravitational Wave Tests of Strong Field General Relativity with Binary Inspirals: Realistic Injections and Optimal Model Selection

Department of Physics, Montana State University, Bozeman, MT 59717, USA.(Dated: March 7, 2013)We study generic tests of strong-field General Relativity using gravitational waves emitted duringthe inspiral of compact binaries. Previous studies have considered simple extensions to the standardpost-Newtonian waveforms that differ by a single term in the phase. Here we improve on thesestudies by (i) increasing the realism of injections and (ii) determining the optimal waveform familiesfor detecting and characterizing such signals. We construct waveforms that deviate from thosein General Relativity through a series of post-Newtonian terms, and find that these higher-orderterms can affect our ability to test General Relativity, in some cases by making it easier to detecta 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 islittle to be gained from using more complicated models with multiple phase terms. The resultsfound here will help guide future attempts to test General Relativity with advanced ground-baseddetectors.

Constraining the Solution to the Last Parsec Problem with Pulsar Timing

The detection of a stochastic gravitational-wave signal from the superposition of many inspiraling supermassive black holes with pulsar timing arrays (PTAs) is likely to occur within the next decade. With this detection will come the opportunity to learn about the processes that drive black-hole-binary systems toward merger through their effects on the gravitational-wave spectrum. We use Bayesian methods to investigate the extent to which effects other than gravitational-wave emission can be distinguished using PTA observations. We show that, even in the absence of a detection, it is possible to place interesting constraints on these dynamical effects for conservative predictions of the population of tightly bound supermassive-black-hole binaries. For instance, if we assume a relatively weak signal consistent with a low number of bound binaries and a low black-hole-mass to galaxy-mass correlation, we still find that a nondetection by a simulated array, with a sensitivity that should be reached in practice within a few years, disfavors gravitational-wave-dominated evolution with an odds ratio of

Mismodeling in gravitational-wave astronomy: The trouble with templates

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Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays

. Such a finding would suggest either that all existing astrophysical models for the population of tightly bound binaries are overly optimistic, or else that some dynamical effect other than gravitational-wave emission is actually dominating binary evolution even at the relatively high frequencies/small orbital separations probed by PTAs.

Towards robust gravitational wave detection with pulsar timing arrays

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 observations 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 directly fit into the simplest parametrized 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 a simple 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 parametrized waveform model that may allow us to test GR using the full inspiral-merger-ringdown signal.

A Rosetta Stone for Parameterized Tests of Gravity

We introduce a technique for gravitational-wave analysis, where Gaussian process regression is used to emulate the strain spectrum of a stochastic background by training on population-synthesis simulations. This leads to direct Bayesian inference on astrophysical parameters. For pulsar timing arrays specifically, we interpolate over the parameter space of supermassive black-hole binary environments, including three-body stellar scattering, and evolving orbital eccentricity. We illustrate our approach on mock data, and assess the prospects for inference with data similar to the NANOGrav 9-yr data release.

Rosetta stone for parametrized tests of gravity

Precision timing of highly stable milli-second pulsars is a promising technique for the detection of very low frequency sources of gravitational waves. In any single pulsar, a stochastic gravitational wave signal appears as an additional source of timing noise that can be absorbed by the noise model, and so it is only by considering the coherent response across a network of pulsars that the signal can be distinguished from other sources of noise. In the limit where there are many gravitational wave sources in the sky, or many pulsars in the array, the signals produce a unique tensor correlation pattern that depends only on the angular separation between each pulsar pair. It is this distinct fingerprint that is used to search for gravitational waves using pulsar timing arrays. Here we consider how the prospects for detection are diminished when the statistical isotropy of the timing array or the gravitational wave signal is broken by having a finite number of pulsars and a finite number of sources. We find the standard tensor-correlation analysis to be remarkably robust, with a mild impact on detectability compared to the isotropic limit. Only when there are very few sources and very few pulsars does the standard analysis begin to fail. Having established that the tensor correlations are a robust signature for detection, we study the use of sky-scrambles to break the correlations as a way to increase confidence in a detection. This approach is analogous to the use of time-slides in the analysis of data from ground based interferometric detectors.

The Trouble With Templates

Several model-independent parameterizations of deviations from General Relativity have been developed to test Einsteins theory. Although these different parameterizations were developed for different gravitational observables, they ultimately all test the same underlying physics. In this paper, we develop connections between the parameterized post-Newtonian, parameterized post-Keplerian, and the parameterized post-Einsteinian frameworks, developed to carry out tests of General Relativity with Solar System, binary pulsar, and gravitational wave observations respectively. These connections allow us to use knowledge gained from one framework to inform and guide tests using the others. Relating these parameterizations and combining the results from each approach strengthens our tests of General Relativity.