Parametrized post-Einsteinian Framework Research Articles

Modeling compact binary merger waveforms beyond general relativity

The parametrized post-Einsteinian framework modifies inspiral waveform models to incorporate effects beyond general relativity (GR). We extend the existing model into the merger-ringdown regime. The modification introduced here adds a single degree of freedom that corresponds to a change in the binary coalescence time. Other merger properties remain as predicted by GR. We discuss parameter estimation with this model, and how it can be used to extract information from beyond-GR waveforms.

Simultaneous bounds on the gravitational dipole radiation and varying gravitational constant from compact binary inspirals

Compact binaries are an important class of gravitational-wave (GW) sources that can be detected by current and future GW observatories. They provide a testbed for general relativity (GR) in the highly dynamical strong-field regime. Here, we use GWs from inspiraling binary neutron stars and binary black holes to investigate dipolar gravitational radiation (DGR) and varying gravitational constant predicted by some alternative theories to GR, such as the scalar-tensor gravity. Within the parametrized post-Einsteinian framework, we introduce the parametrization of these two effects simultaneously into compact binaries' inspiral waveform and perform the Fisher-information-matrix analysis to estimate their simultaneous bounds. In general, the space-based GW detectors can give a tighter limit than ground-based ones. The tightest constraints can reach σB<3×10−11 for the DGR parameter B and σG˙/G<7×10−9yr−1 for the varying G, when the time to coalescence of the GW event is close to the lifetime of space-based detectors. In addition, we analyze the correlation between these two effects and highlight the importance of considering both effects in order to arrive at more realistic results.

Are parametrized tests of general relativity with gravitational waves robust to unknown higher post-Newtonian order effects?

Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general relativity (a realization of the parametrized post-Einsteinian framework), where the gravitational waveform, as calculated in Einstein's theory as a series expansion in the orbital velocity, is parametrically deformed at a given set of orders in velocity. However, most current approaches usually only analyze the data while considering a single, specific modification at a time. Are then constraints placed with a single modification robust to our ignorance of higher post-Newtonian order corrections? We show here that for a wide class of theories, specifically those that admit a post-Newtonian expansion, single-parameter tests are indeed robust. In particular, through a series of full Bayesian parameter estimation studies on several different sets of synthetic data, we show that single-parameter constraints are not degraded but rather are improved by the inclusion of multiple parameters, provided one includes information about the mathematical structure of the series. We then exemplify this with a specific theory of gravity, shift-symmetric scalar Gauss-Bonnet theory, where the waveform has been calculated to higher post-Newtonian orders than leading. We show that the inclusion of these higher order terms strengthens single-parameter constraints, instead of weakening them, and that the strengthening is very mild. This analysis therefore provides strong evidence that single-parameter post-Einsteinian tests of general relativity are robust to ignorance of high post-Newtonian order terms in the general relativistic deformations.

Constrains on the electric charges of the binary black holes with GWTC-1 events

Testing black hole’s charged property is a fascinating topic in modified gravity and black hole astrophysics. In the first Gravitational-Wave Transient Catalog (GWTC-1), ten binary black hole merger events have been formally reported, and these gravitational wave signals have significantly enhanced our understanding of the black hole. In this paper, we try to constrain the amount of electric charge with the parameterized post-Einsteinian framework by treating the electric charge as a small perturbation in a Bayesian way. We find that the current limits in our work are consistent with the result of Fisher information matrix method in previous works. We also develop a waveform model considering a leading order charge effect for binary black hole inspiral.

Constraining gravitational-wave polarizations with Taiji

Space-based gravitational-wave detectors consist of a triangle of three spacecraft, which makes it possible to detect polarization modes of gravitational waves due to the motion of the detectors in space. In this paper we explore the ability of Taiji to detect the polarization modes in the parametrized post-Einsteinian framework. Assuming massive black hole binaries with the total mass of $M=4\times10^5\,M_{\odot}$ at redshift of $z=1$, we find that Taiji can measure the dipole and quadruple emission ($\Delta\alpha_D/\alpha_D$ and $\Delta\alpha_Q/\alpha_Q$) with the accuracy of up to $\sim 0.04\%$, with the fiducial value of $\alpha_D=0.001$, the scalar transverse and longitudinal modes ($\Delta\alpha_B$ and $\Delta\alpha_L$) up to $\sim 0.01$, and the vector modes ($\Delta\alpha_V$) up to $\sim 0.0005$.

Testing massive-field modifications of gravity via gravitational waves

Abstract The direct detection of gravitational waves now provides a new channel for testing gravity theories. Despite that the parametrized post-Einsteinian framework is a powerful tool to quantitatively investigate the effects of modifications to gravity theory, the gravitational waveform in this framework is still extendable. One such extension is to take into account the gradual activation of dipole radiation due to massive fields, which are still only very weakly constrained if their mass $m$ is greater than $10^{-16}$$\,$eV from pulsar observations. Ground-based gravitational-wave detectors (LIGO, Virgo, and KAGRA) are sensitive to this activation in the mass range $10^{-14}$$\,$eV $\lesssim m \lesssim 10^{-13}$$\,$eV. Hence, we discuss a dedicated test for dipole radiation due to a massive field using the LIGO/Virgo collaboration’s open data. In addition, assuming Einstein dilaton Gauss Bonnet (EdGB) type coupling, we combine the results of the analysis of binary black hole events to obtain 90% confidence level constraints on the coupling parameter $\alpha_{\rm EdGB}$ as $\sqrt{\alpha_{\rm EdGB}} \lesssim 2.47$$\,$km for any mass less than $6 \times 10^{-14}$$\,$eV for the first time, including $\sqrt{\alpha_{\rm EdGB}} \lesssim 1.85$$\,$km in the massless limit.

Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays

Pulsar timing arrays are sensitive to gravitational wave perturbations produced by individual supermassive black hole binaries during their early inspiral phase. Modified gravity theories allow for the emission of gravitational dipole radiation, which is enhanced relative to the quadrupole contribution for low orbital velocities, making the early inspiral an ideal regime to test for the presence of modified gravity effects. Using a theory-agnostic description of modified gravity theories based on the parametrized post-Einsteinian framework, we explore the possibility of detecting deviations from General Relativity using simulated pulsar timing array data, and provide forecasts for the constraints that can be achieved. We generalize the {\tt enterprise} pulsar timing software to account for possible additional polarization states and modifications to the phase evolution, and study how accurately the parameters of simulated signals can be recovered. We find that while a pure dipole model can partially recover a pure quadrupole signal, there is little possibility for confusion when the full model with all polarization states is used. With no signal present, and using noise levels comparable to those seen in contemporary arrays, we produce forecasts for the upper limits that can be placed on the amplitudes of alternative polarization modes as a function of the sky location of the source.

Synergy between ground- and space-based gravitational-wave detectors for estimation of binary coalescence parameters

We study the advantage of the co-existence of future ground and space based gravitational wave detectors, in estimating the parameters of a binary coalescence. Using the post-Newtonian waveform for the inspiral of non-spinning neutron star-black hole pairs in circular orbits, we study how the estimates for chirp mass, symmetric mass ratio, and time and phase at coalescence are improved by combining the data from different space-ground detector pairs. Since the gravitational waves produced by binary coalescence also provide a suitable domain where we can study strong field gravity, we also study the deviations from general relativity using the parameterized post-Einsteinian framework. As an example, focusing on the Einstein telescope and DECIGO pair, we demonstrate that there exists a sweet spot range of sensitivity in the pre-DECIGO phase where the best enhancement due to the synergy effect can be obtained for the estimates of the post-Newtonian waveform parameters as well as the modification parameters to general relativity.

Parametrized post-Einsteinian framework for gravitational wave bursts

The population of stellar-mass, compact object binaries that merge with non-negligible eccentricity may be large enough to motivate searches with ground-based gravitational wave detectors. Such events could be exceptional laboratories to test General Relativity in the dynamical, strong-field regime, as a larger fraction of the energy is emitted at high velocities, compared to quasicircular inspirals. A serious obstacle here, however, is the challenge of computing theoretical waveforms for eccentric systems with the requisite accuracy for use in a matched-filter search. The corresponding waveforms are more a sequence of concentrated bursts of energy emitted near periapse than a continuous waveform. Based on this, an alternative approach, stacking excess power over the set of time-frequency tiles coincident with the bursts, was recently suggested as a more practical (though suboptimal) detection strategy. The leading-order ``observable'' that would be inferred from such a detection would be a sequence of discrete numbers characterizing the position and size of each time-frequency tile. In General Relativity, this (possibly large) sequence of numbers is uniquely determined by the small set of parameters describing the binary at formation. In this paper, following the spirit of the parametrized post-Einsteinian framework developed for quasicircular inspiral, we propose a simple, parametrized deformation of the baseline general relativistic burst algorithm for eccentric inspiral events that would allow for model-independent tests of Einstein's theory in this high-velocity, strong-field regime.

Constraining Lorentz-violating, modified dispersion relations with gravitational waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational-wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.

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 Einstein's field equations could result in parameter biases and a loss of detection efficiency. A new class of ``parameterized post-Einsteinian'' waveforms has been proposed to cover this eventuality. Here, we apply the parameterized post-Einsteinian approach to simulated data from a network of advanced ground-based interferometers and from a future space-based interferometer. 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.

Nonspinning black holes in alternative theories of gravity

We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and another that does not. In the latter, we find a deformation to the Schwarzschild metric that solves the modified field equations in the small-coupling approximation. We calculate the event horizon shift, the innermost stable circular orbit shift, and corrections to gravitational waves, mapping them to the parametrized post-Einsteinian framework.

Fundamental theoretical bias in gravitational wave astrophysics and the parametrized post-Einsteinian framework

We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the Universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parametrized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parametrized post-Einsteinian templates for the binary coalescence of equal-mass, nonspinning compact objects in a quasicircular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.