Constraining Lorentz-violating, modified dispersion relations with gravitational waves

The growing catalog of gravitational wave (GW) detections by the LIGO-Virgo-KAGRA collaboration enables increasingly stringent tests of general relativity, particularly regarding possible violations of parity and Lorentz symmetry. Parity and Lorentz violations in gravity can modify both the damping rate and dispersion relation of GWs, leading to birefringence, frequency-dependent damping, and dispersion effects in the propagation of GWs. These effects result in amplitude and phase corrections of the waveforms of GWs produced by the coalescence of compact binaries, which enable us to constrain parity- and Lorentz-violating effects by analyzing GW signals detected by LIGO-Virgo-KAGRA detectors with the distorted waveforms. While most current analyses employ single-parameter methods-varying one deformation parameter at a time-modified gravity theories often predict multiple, coexisting deviations. In this work, we construct several specific multi-parameter GW waveform models incorporating parity- and Lorentz-violating effects and perform full Bayesian parameter estimation to compare multi-parameter and single-parameter constraints. We find that including multiple deformation parameters yields constraints on individual parameters that are generally comparable to those from single-parameter analyses, despite one specific model showing a degeneracy between the deformation parameters. Our results support the robustness of single-parameter tests for parity and Lorentz symmetry of gravity in current and future GW observations.

The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation. Such variations have the potential to affect both the generation and propagation of gravitational waves. Here, our focus lies on the effect of gravitational constant variation specifically on the propagation of gravitational waves. In a previous paper (An et al., 2023 [13]) we have studied such effect based on a Maxwell-like equation. That work admits two drawbacks. The assumption that describing gravitational waves with Maxwell-like equation is not solid. And more such treatment can only deal with space dependent gravitational constant. In the current paper we will remedy these two issues. We employ two analytical methods, namely based on the Fierz-Pauli action and the perturbation of Einstein-Hilbert action around Minkowski spacetime, both leading to the same gravitational wave equation. By solving this equation, we find the effects of gravitational constant variation on gravitational wave propagation. The result is consistent with previous investigations based on Maxwell-like equations for gravitational waves for space dependent gravitational constant cases. In addition we can constrain the time variation of the gravitational constant via the propagation of gravitational waves based on GW170817 data. And more, we find that small variations in the gravitational constant result in an amplitude correction at the leading order and a phase correction at the sub-leading order for gravitational waves. These results provide valuable insights for probing gravitational constant variation and can be directly applied to gravitational wave data analysis.

The authors investigate the propagation of small-amplitude gravitational waves through pressureless matter ('dust'). After establishing the local linearisation stability of Einstein's equation for dust about any of its solutions they use the WKB method to study the locally plane, linearised perturbations of an arbitrary background dust spacetime asymptotically for small wavelengths. The dispersion relation exhibits two modes. One is simply degenerate and represents gravitational waves, whereas the other is doubly degenerate and describes density and vorticity perturbations. The waves are shown to propagate along the null geodesics of the background; in leading WKB order their amplitudes behave as in vacuo. The rays associated with the matter mode are the wordlines of the background dust. In leading order the perturbations of density and 4-velocity vanish for both modes.

Since the first detection of gravitational waves, they have been used to investigate various fundamental problems, including the variation of physical constants. Regarding the gravitational constant, previous works focused on the effect of the gravitational constant variation on the gravitational wave generation. In this paper, we investigate the effect of the gravitational constant variation on the gravitational wave propagation. The Maxwell-like equation that describes the propagation of gravitational waves is extended in this paper to account for situations where the gravitational constant varies. Based on this equation, we find that the amplitude of gravitational waves will be corrected. Consequently the estimated distance to the gravitational wave source without considering such a correction may be biased. Applying our correction result to the well known binary neutron star coalescence event GW170817, we get a constraint on the variation of the gravitational constant. Relating our result to the Yukawa deviation of gravity, we for the first time get the constraint of the Yukawa parameters in 10 Mpc scale. This scale corresponds to a graviton mass mg∼10−31 eV.

Scalar-tensor theories leaving significant modifications of gravity at cosmological scales rely on screening mechanisms to recover general relativity (GR) in high-density regions and pass stringent tests with astrophysical objects. Much focus has been placed on the signatures of such modifications of gravity on the propagation of gravitational waves (GWs) through cosmological distances while typically assuming their emission from fully screened regions with the wave generation strictly abiding by GR. Here, we closely analyze the impact of screening mechanisms on the inspiral GW waveforms from compact sources by employing a scaling method that enables a post-Newtonian (PN) expansion in screened regimes. Particularly, we derive the leading-order corrections to a fully screened emission to first PN order in the near zone, and we also compute the modifications in the unscreened radiation zone to second PN order. For a concrete example, we apply our results to a cubic Galileon model. The resulting GW amplitude from a binary black hole inspiral deviates from its GR counterpart at most by one part in ${10}^{2}$ for the modifications in the radiation zone and at most one part in ${10}^{11}$ due to next-order corrections to the fully screened near zone. We expect such modifications to be undetectable by the current generation of GW detectors, but the deviation is not so small as to remain undetectable in future experiments.

In testing gravity a model-independent way, one of crucial tests is measuring the propagation speed of a gravitational wave (GW). In general relativity, a GW propagates with the speed of light, while in the alternative theories of gravity the propagation speed could deviate from the speed of light due to the modification of gravity or spacetime structure at a quantum level. Previously we proposed the method measuring the GW speed by directly comparing the arrival times between a GW and a photon from the binary merger of neutron stars or neutron star and black hole, assuming that it is associated with a short gamma-ray burst. The sensitivity is limited by the intrinsic time delay between a GW and a photon at the source. In this paper, we extend the method to distinguish the intrinsic time delay from the true signal caused by anomalous GW speed with multiple events at cosmological distances, also considering the redshift distribution of GW sources, redshift-dependent GW propagation speed, and the statistics of intrinsic time delays. We show that an advanced GW detector such as Einstein Telescope will constrain the GW propagation speed at the precision of ~10^{-16}. We also discuss the optimal statistic to measure the GW speed, performing numerical simulations.

The extreme sensitivity required for direct observation of gravitational waves by the Advanced LIGO detectors means that environmental noise is increasingly likely to contaminate Advanced LIGO gravitational wave signals if left unaddressed. Consequently, environmental monitoring efforts have been undertaken and novel noise mitigation techniques have been developed which have reduced environmental coupling and made it possible to analyze environmental artifacts with potential to affect the 90 gravitational wave events detected from 2015–2020 by the Advanced LIGO detectors. So far, there is no evidence for environmental contamination in gravitational wave detections. However, automated, rapid ways to monitor and assess the degree of environmental coupling between gravitational wave detectors and their surroundings are needed as the rate of detections continues to increase. We introduce a computational tool, PEMcheck, for quantifying the degree of environmental coupling present in gravitational wave signals using data from the extant collection of environmental monitoring sensors at each detector. We study its performance when applied to 79 gravitational waves detected in LIGO’s third observing run and test its performance in the case of extreme environmental contamination of gravitational wave data. We find that PEMcheck’s automated analysis identifies only a small number of gravitational waves that merit further study by environmental noise experts due to possible contamination, a substantial improvement over the manual vetting that occurred for every gravitational wave candidate in the first two observing runs. Building on a first attempt at automating environmental coupling assessments used in the third observing run, this tool represents an improvement in accuracy and interpretability of coupling assessments, reducing the time needed to validate gravitational wave candidates. With the validation provided herein; PEMcheck will play a critical role in event validation during LIGO’s fourth observing run as an integral part of the data quality report produced for each gravitational wave candidate.

In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the Right-handed mode and the Left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard $F(R)$ gravity.

The detection of gravitational wave (GW) has opened a new window to test the theory of gravity in the strong field regime. In general relativity (GR), GW can only possess two tensor polarization modes, which are known as the $+$ and $\times$ modes. However, vector and scalar modes can exist in some modified theories of gravity, and we can test the gravitational theories by probing these extra polarization modes. As a space-borne GW detector, TianQin will be launched in the 2030s, and it is expected to observe plenty of GW signals, including those from nearly ten-thousands double white dwarfs (DWDs) in our galaxy. This offers an excellent chance for testing the existence of extra polarization modes. In this article, we analyze the capability of detecting the extra polarization modes with DWDs. For the extra modes, we consider both the leading order dipole radiation and the subleading quadrupole radiation. We find that the capability of TianQin has very strong dependency on the source orientation. We also analyze all the verification binaries with determined position and frequency, and find that ZTF J1539 can give the best constraint on the extra polarization modes. We have also considered the case of TianQin twin constellation, and the joint observation with LISA.

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Modified dispersion relations(MDRs) as a manifestation of Lorentz invariance violation, have been appeared in alternative approaches to quantum gravity problem. Loop quantum gravity is one of these approaches which evidently requires modification of dispersion relations. These MDRs will affect the usual formulation of the Compton effect. The purpose of this paper is to incorporate the effects of loop quantum gravity MDRs on the formulation of Compton scattering. Using limitations imposed on MDRs parameters from Ultra High Energy Cosmic Rays(UHECR), we estimate the quantum gravity-induced wavelength shift of scattered photons in a typical Compton process. Possible experimental detection of this wavelength shift will provide strong support for underlying quantum gravity proposal.

This thesis investigates the direct measurement of the thermal noise spectral distribution. Long base line gravitational wave detectors, being commissioned around the world, are limited in sensitivity in the intermediate frequencies by the thermal noise. These detectors are utilising suspended test mirrors for the detection of gravitational waves by measuring their relative displacement. One of the fundamental noise sources in these detectors is the thermally induced displacement of the suspension onto and within the mirrors. This thermally induced motion of the test mirrors limits the displacement sensitivity of the gravitational wave detectors. Knowledge of the spectral behavior of thermal noise over a wide frequency range will improve predictions and understanding of the behavior of the suspension and test mirrors. ¶ In this thesis the direct measurement of the thermal noise spectral distribution of a mechanical flexure resonator is described. The mechanical flexure resonator is an unidirectional ’wobbly table’ made from copper-beryllium, which hinges around four thin flexures 15 mm wide, 1 mm high and ~116 µm thick. The mechanical flexure resonator has a resonant frequency of 192 Hz, with a quality factor of ~3000. ¶ ...

The proposed TianQin gravitational wave observatory is aiming to detect gravitational wave signals in the millihertz frequency band, through the method of space-borne laser interferometry. In total, three satellites will be launched, each following a geocentric orbit, with an orbital altitude of about one hundred thousand kilometers. They form into an equilateral triangle formation, with an orbital period of <sc>3.6 d.</sc> The orbital plane of TianQin is fixed almost constant, towards one specific gravitational wave source, RXJ0806.3+1527, so that TianQins response to this source is maximized, and this source can be used to calibrate and assess the facilities performance. It is widely anticipated that in the millihertz frequency band, there lurks a wide variety of gravitational wave sources, ranging from massive black hole binary mergers, extreme mass ratio inspirals, Galactic binary white dwarves, stellar mass binary compact objects inspirals, as well as stochastic gravitational wave background. Meanwhile, the expected source number in such frequency band would also be huge. The successful implementation of the TianQin project would pave the way towards exciting prospects of future gravitational wave research. By successfully performing gravitational wave observation, the TianQin gravitational wave observatory can open a new window for the study of gravitational wave astronomy, gravitational wave cosmology as well as gravitational wave physics. The science prospect of TianQin gravitational wave observation can be further enhanced through a combination with multi-band gravitational wave detection and multi-messenger astronomical observations, by collaboration with gravitational wave detectors operating in different frequency bands as well as with other probes focusing on different messengers like electro-magnetic signals, neutrinos or cosmic rays. The TianQin project will also greatly promote the construction of a high-precision space-time reference system, ultra-long-range laser interferometry, high-precision satellite platform, etc. The development of cutting-edge space technologies has important applications in the national economy as well as the national strategic needs. Currently, the TianQin project has made important progress in the precision gravity measurement facility, the payload research base, the laser ranging station, the simulation facility for space-borne gravitation wave detection on ground, and the series test satellite for the TianQin project. Based on the long-term accumulation of relevant technology, the TianQin project team proposed the goal of achieving gravitational wave detection in the 2030s, and a 0123 plan roadmap is formulated, aiming to perform, step by step, lunar or relay satellite laser ranging, testing key technology like space-borne laser interferometry and drag-free control, verifying high precision space-borne laser interferometry technology, and ultimately detecting gravitational wave. By the 2030s, the scientific cooperation between scientists from all over the world and the use of various means to jointly conduct exploration and research on the Universe will face great development. So far, the TianQin project has held many international seminars and received extensive international attention and active participation. Currently, the TianQin Collaboration Group has been formally established, with a collaboration group advisory committee also established, consisting of scientists with significant influence in the field of gravitational wave detection all over the world. The TianQin project will establish a collaborative research or comprehensive cooperation agreement with foreign universities or research organizations, and vigorously promote the China-led space-borne gravitational wave detection business. Through extensive international cooperation, the TianQin project will unite domestic and foreign strengths and strive to take the lead in realizing the gravitational wave detection in the window of millihertz band.

The direct detection of gravitational waves (GW) from merging binary black holes and neutron stars mark the beginning of a new era in gravitational physics, and it brings forth new opportunities to test theories of gravity. To this end, it is crucial to search for anomalous deviations from general relativity in a model-independent way, irrespective of gravity theories, GW sources, and background spacetimes. In this paper, we propose a new universal framework for testing gravity with GW, based on the generalized propagation of a GW in an effective field theory that describes modification of gravity at cosmological scales. Then we perform a parameter estimation study, showing how well the future observation of GW can constrain the model parameters in the generalized models of GW propagation.

Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the latter is currently analyzed on the basis of the available observational data from gamma-ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.