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In gravitational-wave astronomy, extreme-mass-ratio-inspiral (EMRI) sources for the upcoming LISA observatory have the potential to serve as high-precision probes of astrophysical environments in galactic nuclei, and of potential deviations from general relativity (GR). Such “beyond vacuum-GR” effects are often modeled as perturbations to the evolution of vacuum EMRIs under GR. Many studies have reported unprecedented constraints on these effects by examining the inference of one effect at a time. However, in a more realistic analysis, the simultaneous inference of multiple such effects is required since the parameters describing them are generally significantly correlated with each other and the vacuum EMRI parameters. Here, in a general framework, we show that these correlations remain even if any modeled effect is absent in the actual signal, and that they cause inference bias when any effect in the signal is ignored in the analysis model. This worsens the overall measurability of the whole parameter set, challenging the constraints found by previous studies, and posing a general problem for the modeling and inference of beyond vacuum-GR effects in EMRIs.

We seek to achieve the holy grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior $p(\theta |D)$ for the source parameters $\theta$, given the detector data $D$. To do so, we train a deep neural network to take as input a signal + noise dataset (drawn from the astrophysical source-parameter prior and the sampling distribution of detector noise), and to output a parametrized approximation of the corresponding posterior. We rely on a compact representation of the data based on reduced-order modeling, which we generate efficiently using a separate neural-network waveform interpolant [A. J. K. Chua, C. R. Galley, and M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019)]. Our scheme has broad relevance to gravitational-wave applications such as low-latency parameter estimation and characterizing the science returns of future experiments.

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster but approximate ones. The model error introduced by this substitution can be mitigated in various ways, one of which is by interpolating and marginalizing over the error using Gaussian-process regression. However, the use of Gaussian-process regression is limited by the curse of dimensionality, which makes it less effective for analyzing higher-dimensional parameter spaces and longer signal durations. In this work, to address this limitation, we focus on gravitational-wave signals from extreme-mass-ratio inspirals as an example, and propose several significant improvements to the base method: an improved prescription for constructing the training set, graphics processing units-accelerated training algorithms, and a new likelihood that better adapts the base method to the presence of detector noise. Our results suggest that the new method is more viable for the analysis of realistic gravitational-wave data.

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). As an example, we apply this technique to the measurement of chirp mass using (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behavior for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalized likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood both in our simple one-dimensional study, and theoretically in general. We also examine the dependence of the method on the size of training set used in the GPR; on the form of covariance function adopted for the GPR, and on changes to the detector noise power spectral density.

The Laser Interferometer Space Antenna (LISA) is slated for launch in the early 2030s. A main target of the mission is massive black hole binaries that have an expected detection rate of $\sim 20{\mathrm{yr}}^{-1}$. We present a parameter estimation analysis for a variety of massive black hole binaries. This analysis is performed with a graphics processing unit (GPU) implementation comprising the phenomhm waveform with higher-order harmonic modes and aligned spins; a fast frequency-domain LISA detector response function; and a GPU-native likelihood computation. The computational performance achieved with the GPU is shown to be 500 times greater than with a similar CPU implementation, which allows us to analyze full noise-infused injections at a realistic Fourier bin width for the LISA mission in a tractable and efficient amount of time. With these fast likelihood computations, we study the effect of adding aligned spins to an analysis with higher-order modes by testing different configurations of spins in the injection, as well as the effect of varied and fixed spins during sampling. Within these tests, we examine three different binaries with varying mass ratios, redshifts, sky locations, and detector-frame total masses ranging over 3 orders of magnitude. We discuss varied correlations between the total masses and mass ratios; unique spin posteriors for the larger mass binaries; and the constraints on parameters when fixing spins during sampling, allowing us to compare to previous analyses that did not include aligned spins.

The analysis of gravitational-wave (GW) datasets is based on the comparison of measured time series with theoretical templates of the detector’s response to a variety of source parameters. For the Laser Interferometer Space Antenna (LISA), the main scientific observables will be the so-called time-delay interferometry (TDI) combinations, which suppress the otherwise overwhelming laser noise. Computing the TDI response to GWs involves projecting the GW polarizations onto the LISA constellation arms, and then combining projections delayed by a multiple of the light propagation time along the arms. Both computations are difficult to perform efficiently for generic LISA orbits and GW signals. Various approximations are currently used in practice, e.g., assuming constant and equal arm lengths, which yields analytical TDI expressions that are essential to the desirable speed of current analysis codes. In this article, we present fastlisaresponse, a new efficient graphics-processing-unit-accelerated code designed to perform systematics studies on the LISA response in a fully Bayesian context. We examine loud Galactic binary signals first with the typical equal-arm-length approximation and then with a hybrid template that uses accurate orbits for the projections and equal-arm-length orbits for the TDI combinations. The hybrid template is an attempt to preserve the efficient analytical TDI expressions. We conclude that all equal-arm-length parameter-estimation codes, including when only used for TDI, need to be upgraded to the generic response if they are to achieve optimal accuracy for high (but reasonable) SNR sources within the actual LISA data.

Scientific analysis for the gravitational wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary inclination and black hole spin, up to modest eccentricity ($\lesssim 0.3$) and separation ($\gtrsim 2–10\mathrm{M}$ from the last stable orbit). In that regime, our waveforms are accurate at the leading “adiabatic” order, and they approximately capture transient self-force resonances that significantly impact the gravitational wave phase. The model fills an urgent need for extensive waveforms in ongoing data-analysis studies, and its individual components will continue to be useful in future science-adequate waveforms.

Gravitational waves from a source moving relative to us can suffer from special-relativistic effects such as aberration. The required velocities for these to be significant are on the order of $1000\mathrm{km}{\mathrm{s}}^{-1}$. This value corresponds to the velocity dispersion that one finds in clusters of galaxies. Hence, we expect a large number of gravitational-wave sources to have such effects imprinted in their signals. In particular, the signal from a moving source will have its higher modes excited, i.e., (3,3) and beyond. We derive expressions describing this effect and study its measurability for the specific case of a circular, nonspinning extreme-mass-ratio inspiral. We find that the excitation of higher modes by a peculiar velocity of $1000\mathrm{km}{\mathrm{s}}^{-1}$ is detectable for such inspirals with signal-to-noise ratios of $\gtrsim 20$. Using a Fisher matrix analysis, we show that the velocity of the source can be measured to a precision of just a few percent for a signal-to-noise ratio of 100. If the motion of the source is ignored, parameter estimates could be biased, e.g., the estimated masses of the components through a Doppler shift. Conversely, by including this effect in waveform models, we could measure the velocity dispersion of clusters of galaxies at distances inaccessible to light.

Extreme mass ratio inspirals (EMRIs) are key sources for the future space-based gravitational wave detector Laser Interferometer Space Antenna (LISA) and are considered promising probes of fundamental physics. Here, we present the first complete Bayesian analysis of EMRI signals in theories with an additional massless scalar, which could arise in an extension of general relativity or of the Standard Model of particle physics. We develop a waveform model accurate at adiabatic order for equatorial eccentric orbits around spinning black holes. Using full Bayesian inference, we forecast LISA’s ability to probe the presence of new fundamental fields with EMRI observations.

We apply Hall and Reginatto's theory of interacting classical and quantum ensembles to harmonically coupled particles, with a view to understanding its experimental implications. This hybrid theory has no free parameters and makes distinctive predictions that should allow it to be experimentally distinguished from quantum mechanics. It also bears on the questions of quantum measurement and quantum gravity.

A gravitational-wave background can be detected in pulsar-timing-array data as Hellings-Downs correlations among the timing residuals measured for different pulsars. The optimal statistic implements this concept as a classical null-hypothesis statistical test: a null model with no correlations can be rejected if the observed value of the statistic is very unlikely under that model. To address the dependence of the statistic on the uncertain pulsar noise parameters, the pulsar-timing-array community has adopted a hybrid classical-Bayesian scheme [S. J. Vigeland et al., Phys. Rev. D 98, 044003 (2018).] in which the posterior distribution of the noise parameters induces a posterior distribution for the statistic. In this article we propose a rigorous interpretation of the hybrid scheme as an instance of posterior predictive checking, and we introduce a new summary statistic (the Bayesian signal-to-noise ratio) that should be used to accurately quantify the statistical significance of an observation instead of the mean posterior signal-to-noise ratio, which does not support such a direct interpretation. In addition to falsifying the no-correlation hypothesis, the Bayesian signal-to-noise ratio can also provide evidence supporting the presence of Hellings-Downs correlations. We demonstrate our proposal with simulated datasets based on NANOGrav’s 12.5-yr data release. We also establish a relation between the posterior distribution of the statistic and the Bayes factor in favor of correlations, thus calibrating the Bayes factor in terms of hypothesis-testing significance.

Extreme-mass-ratio inspirals (EMRIs) are one of the most exciting and promising target sources for space-based interferometers (such as LISA, Taiji, and TianQin). The observation of their emitted gravitational waves will offer stringent tests on general theory of relativity and provide a wealth of information about the dense environment in galactic centers. To unlock such potential, it is necessary to correctly characterize EMRI signals. However, resonances are a phenomena that occurs in EMRI systems and can impact parameter inference, and therefore the science outcome, if not properly modeled. Here, we explore how to model resonances and develop an efficient implementation. Our previous work has demonstrated that tidal resonances induced by the tidal field of a nearby astrophysical object alters the orbital evolution, leading to a significant dephasing across observable parameter space. Here, we extensively explore a more generic model for the tidal perturber with additional resonance combinations, to study the dependence of resonance strength on the intrinsic orbital and tidal parameters. To analyze the resonant signals, accurate templates that correctly incorporate the effects of the tidal field are required. The evolution through resonances is obtained using a step function, whose amplitude is calculated using an analytic interpolation of the resonance jumps. We benchmark this procedure by comparing our approximate method to a numerical evolution. We find that there is no significant error caused by this simplified prescription, as far as the astronomically reasonable range in the parameter space is concerned. Further, we use Fisher matrices to study both the measurement precision of parameters and the systematic bias due to inaccurate modeling. Modeling of self-force resonances can also be carried out using the implementation presented in this study, which will be crucial for EMRI waveform modeling.

A binary extreme-mass-ratio inspiral (b-EMRI) is a hierarchical triple system consisting of a stellar-mass binary black hole (BBH) orbiting a central Kerr supermassive black hole (SMBH). Although predicted by several astrophysical models, b-EMRIs pose a challenge in waveform modeling due to their complex three-body dynamics and strong relativistic effects. Here we take advantage of the hierarchical nature of b-EMRI systems to transform the internal motion of the small binary into global trajectories around the SMBH. This allows us to use black hole perturbation theory to calculate both the low-frequency gravitational waveform due to its EMRI nature and the high-frequency waveform generated by the inner motion of the BBH. When the inner binary’s separation vanishes, our calculation recovers the standard relativistic adiabatic EMRI waveform. Furthermore, by including the high-frequency perturbation, we find a correction to the waveform as large as the adiabatic order when the frequency matches the quasinormal modes (QNMs) of the SMBH, therefore supporting an earlier proof-of-concept study claiming that the small BBH can resonantly excite the QNMs of the SMBH. More importantly, we find that b-EMRIs can evolve faster than regular EMRIs due to this resonant dissipation through the high-frequency modes. These characteristics distinguish b-EMRI waveform templates from regular EMRI templates for future space-based gravitational wave detectors.

Extreme mass ratio inspirals (EMRIs) will be important sources for future space-based gravitational-wave detectors. In recent work, tidal resonances in binary orbital evolution induced by the tidal field of nearby stars or black holes have been identified as being potentially significant in the context of extreme mass-ratio inspirals. These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a “jump” leading to a shift in the phase of the gravitational waveform. In this paper, we treat the tidal perturber as stationary and restricted to the equatorial plane, and present a first study of how common and important such resonances are over the entire orbital parameter space. We find that a large proportion of inspirals encounter a low-order resonance in the observationally important regime. While the “instantaneous” effect of a tidal resonance is small, its effect on the accumulated phase of the gravitational waveform of an EMRI system can be significant due to its many cycles in band; we estimate that the effect is detectable for a significant fraction of sources. We also provide fitting formulas for the induced change in the constants of motion of the orbit due to the tidal resonance for several low-order resonances.

We present the fastemriwaveforms (FEW) package, a collection of tools to build and analyze extreme mass ratio inspiral (EMRI) waveforms. Here, we expand on [A. J. K. Chua et al., Phys. Rev. Lett. 126, 051102 (2021).] that introduced the first fast and accurate fully-relativistic EMRI waveform template model. We discuss the construction of the overall framework; constituent modules; and the general methods used to accelerate EMRI waveforms. Because the fully relativistic FEW model waveforms are for now limited to eccentric orbits in the Schwarzschild spacetime, we also introduce an improved augmented analytic kludge (AAK) model that describes generic Kerr inspirals. Both waveform models can be accelerated using graphics processing unit (GPU) hardware. With the GPU-accelerated waveforms in hand, a variety of studies are performed including an analysis of EMRI mode content, template mismatch, and fully Bayesian Markov Chain Monte Carlo-based EMRI parameter estimation. We find relativistic EMRI waveform templates can be generated with fewer harmonic modes ($\sim 10–100$) without biasing signal extraction. However, we show for the first time that extraction of a relativistic injection with semirelativistic amplitudes can lead to strong bias and anomalous structure in the posterior distribution for certain regions of parameter space.

One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localization of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and especially in the analysis of data from future space-based detectors such as eLISA, for which online grid searches are difficult due to the long-duration waveforms and large parameter spaces.

We present ENIGMA, a time domain, inspiral-merger-ringdown waveform model that describes nonspinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasicircular merger, which is constructed using machine learning algorithms that are trained with quasicircular numerical relativity waveforms. We show that ENIGMA reproduces with excellent accuracy the dynamics of quasicircular compact binaries. We validate ENIGMA using a set of Einstein Toolkit eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between $1\le q\le 5.5$, and eccentricities $e_0\lesssim 0.2$ ten orbits before merger. We use this model to explore in detail the physics that can be extracted with moderately eccentric, nonspinning binary black hole mergers. In particular, we use ENIGMA to show that the gravitational wave transients GW150914, GW151226, GW170104, GW170814 and GW170608 can be effectively recovered with spinning, quasicircular templates if the eccentricity of these events at a gravitational wave frequency of 10 Hz satisfies $e_0\le \{0.175,0.125,0.175,0.175,0.125\}$, respectively. We show that if these systems have eccentricities $e_0\sim 0.1$ at a gravitational wave frequency of 10 Hz, they can be misclassified as quasicircular binaries due to parameter space degeneracies between eccentricity and spin corrections. Using our catalog of eccentric numerical relativity simulations, we discuss the importance of including higher-order waveform multipoles in gravitational wave searches of eccentric binary black hole mergers.

Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms are first represented as weighted sums over reduced bases (reduced-order modeling); we then train artificial neural networks to map gravitational-wave source parameters into basis coefficients. Statistical inference proceeds directly in coefficient space, where it is theoretically straightforward and computationally efficient. The neural networks also provide analytic waveform derivatives, which are useful for gradient-based sampling schemes. We demonstrate fast and accurate coefficient interpolation for the case of a four-dimensional binary-inspiral waveform family and discuss promising applications of our framework in parameter estimation.

We compute adiabatic waveforms for extreme mass-ratio inspirals (EMRIs) by “stitching” together a long inspiral waveform from a sequence of waveform snapshots, each of which corresponds to a particular geodesic orbit. We show that the complicated total waveform can be regarded as a sum of “voices.” Each voice evolves in a simple way on long timescales, a property which can be exploited to efficiently produce waveform models that faithfully encode the properties of EMRI systems. We look at examples for a range of different orbital geometries: spherical orbits, equatorial eccentric orbits, and one example of generic (inclined and eccentric) orbits. To our knowledge, this is the first calculation of a generic EMRI waveform that uses strong-field radiation reaction. We examine waveforms in both the time and frequency domains. Although EMRIs evolve slowly enough that the stationary phase approximation (SPA) to the Fourier transform is valid, the SPA calculation must be done to higher order for some voices, since their instantaneous frequency can change from chirping forward ($\dot{f}>0$) to chirping backward ($\dot{f}<0$). The approach we develop can eventually be extended to more complete EMRI waveform models—for example, to include effects neglected by the adiabatic approximation, such as the conservative self-force and spin-curvature coupling.