Constraints on parity and Lorentz violations from gravitational waves: A comparison between single-parameter and multi-parameter analysis

The properties of gravitational-wave (GW) propagation are modified in alternative theories of gravity and are crucial observables to test gravity at cosmological distance. The propagation speed has already been measured from GW170817 so precisely and pinned down to the speed of light, while other properties of GW propagation have not constrained tightly yet. In this paper, we investigate the measurement precisions of the amplitude damping rate (equivalently, the time variation of the gravitational coupling for GWs) and graviton mass in the generalized framework of GW propagation with the future detectors such as Voyager, Cosmic Explorer, and Einstein Telescope. As a result, we show that the future GW observation can reach 1% error for the amplitude damping. We also study the time variation of the gravitational couplings in Horndeski theory by performing Monte Carlo-based numerical simulations. From the simulation results, we find that the current accelerating Universe prefers the models with less damping of GWs and that the equivalence principle can be tested at the level of 1% by the future GW observation.

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.

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.

The nonlinear memory effect is a fascinating prediction of general relativity (GR), in which oscillatory gravitational-wave (GW) signals are generically accompanied by a monotonically-increasing strain which persists in the detector long after the signal has passed. This effect is directly accessible to GW observatories, and presents a unique opportunity to test GR in the dynamical and nonlinear regime. In this article we calculate, for the first time, the nonlinear memory signal associated with GW bursts from cusps and kinks on cosmic string loops, which are an important target for current and future GW observatories. We obtain analytical waveforms for the GW memory from cusps and kinks, and use these to calculate the ‘memory of the memory’ and other higher-order memory effects. These are among the first memory observables computed for a cosmological source of GWs, with previous literature having focused almost entirely on astrophysical sources. Surprisingly, we find that the cusp GW signal diverges for sufficiently large loops, and argue that the most plausible explanation for this divergence is a breakdown in the weak-field treatment of GW emission from the cusp. This shows that previously-neglected strong gravity effects must play an important rôle near cusps, although the exact mechanism by which they cure the divergence is not currently understood. We show that one possible resolution is for these cusps to collapse to form primordial black holes (PBHs); the kink memory signal does not diverge, in agreement with the fact that kinks are not predicted to form PBHs. Finally, we investigate the prospects for detecting memory from cusps and kinks with current and future GW observatories, considering both individual memory bursts and the contribution of many such bursts to the stochastic GW background. We find that in the scenario where the cusp memory divergence is cured by PBH formation, the memory signal is strongly suppressed and is not likely to be detected. However, alternative resolutions of the cusp divergence may in principle lead to much more favourable observational prospects.

This paper reports a comprehensive study on the gravitational wave (GW) background from compact binary coalescences. We consider in our calculations newly available observation-based neutron star and black hole mass distributions and complete analytical waveforms that include post-Newtonian amplitude corrections. Our results show that: (i) post-Newtonian effects cause a small reduction in the GW background signal; (ii) below 100 Hz the background depends primarily on the local coalescence rate $r_0$ and the average chirp mass and is independent of the chirp mass distribution; (iii) the effects of cosmic star formation rates and delay times between the formation and merger of binaries are linear below 100 Hz and can be represented by a single parameter within a factor of ~ 2; (iv) a simple power law model of the energy density parameter $\Omega_{GW}(f) ~ f^{2/3}$ up to 50-100 Hz is sufficient to be used as a search template for ground-based interferometers. In terms of the detection prospects of the background signal, we show that: (i) detection (a signal-to-noise ratio of 3) within one year of observation by the Advanced LIGO detectors (H1-L1) requires a coalescence rate of $r_0 = 3 (0.2) Mpc^{-3} Myr^{-1}$ for binary neutron stars (binary black holes); (ii) this limit on $r_0$ could be reduced 3-fold for two co-located detectors, whereas the currently proposed worldwide network of advanced instruments gives only ~ 30% improvement in detectability; (iii) the improved sensitivity of the planned Einstein Telescope allows not only confident detection of the background but also the high frequency components of the spectrum to be measured. Finally we show that sub-threshold binary neutron star merger events produce a strong foreground, which could be an issue for future terrestrial stochastic searches of primordial GWs.

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 field of gravitational wave astronomy is still in its early stages, with published detections of compact binary coalescences numbering 14 and the most recent observing run (O3) providing 50 more candidates. Another possible source of gravitational waves is rapidly rotating neutron stars which can emit gravitational waves if they have some asymmetry around their rotation axis. These are predicted to emit long duration quasi-sinusoidal signals known as continuous gravitational waves. All-sky and wide parameter space searches for continuous gravitational waves are generally template-matching schemes which test a bank of signal waveforms against data from a gravitational wave detector. Often these searches are highly-tuned to specific signal types and are computationally expensive. We have developed a search method (entitled SOAP) based on the Viterbi algorithm which is model-agnostic and has a computational cost several orders of magnitude lower than template methods and with a comparable sensitivity. In particular, this method can search for signals which have an unknown frequency evolution. We test the algorithm on three simulated and real data sets: gapless Gaussian noise, Gaussian noise with gaps and real data from the final run of initial LIGO (S6). We show that at 95% efficiency, with a 1% false alarm rate, the algorithm achieves a sensitivity of 60, 72 and 74 in the optimal coherent signal to noise ratio in each of these datasets. We discuss the use of this algorithm for detecting a wide range of quasi-monochromatic gravitational wave signals and instrumental artefacts, and demonstrate that it can also identify shorter duration signals such as compact binary coalescences. Many continuous gravitational wave searches are affected by instrumental lines as the long duration narrowband nature of a line can appear to be very similar to a real continuous gravitational wave signal. This has led to the development of techniques to try and limit the effect of instrumental lines, which mostly involve developing a statistic to penalise signals that appear in only a single detector. Whilst these statistics limit the effect of instrumental lines, in the SOAP search described above, many lines still contaminate the statistics and have to be manually removed by investigating other search outputs. We have developed a method using convolutional neural networks to reduce the impact of instrumental artefacts on the SOAP search described above. This has the ability to identify features in each of the detectors spectrograms such that a frequency band can be classified into a signal or noise class. This limits the amount of manual investigation of frequency bands and allowed the SOAP search to be fully automated without a reduction in the sensitivity. Once a continuous gravitational wave is detected, we would want to extract some parameters associated with the source to help understand more about its structure and evolution. We describe a Bayesian method which extracts the sky location, frequency, frequency derivative and signal to noise ratio of a source associated with the frequency evolution returned by the SOAP algorithm. This has the aim of limiting the size of the parameter space for a more sensitive fully coherent follow up search. We tested this approach on 200 simulations in Gaussian noise, generating posterior distributions for the parameters described above. In 90% of these simulations we limit the sky area to 45 deg^2 with a 95% confidence contour. However, we find that this contour contains the true parameter only 42% of the time. We present these results and describe the features and shortcomings of our approach. As mentioned above, we limit the effect of instrumental lines on the SOAP search using machine learning, however we can also identify and mitigate these lines separately before a search is run. We demonstrate how we can use SOAP in a simple configuration to identify instrumental lines. We compare this method to existing line identification tools used in the LIGO collaboration, and find that using the Viterbi statistic SOAP identifies 37% of the same lines as these methods, where for many of the lines which were not identified, other SOAP outputs do show evidence of a line. With further investigation, we expect to identify many more lines in common with existing methods. As well as these common lines, the SOAP algorithm returned 150 more 0.1 Hz wide bands which potentially contain an instrumental line and did not appear on LIGO line-lists.

Gravitational waves (GWs) from compact binary mergers have emerged as one of the most promising probes of cosmology and general relativity (GR). However, a major challenge in fully exploiting GWs as “standard sirens” with current and future GW observatories is developing efficient and robust codes capable of analyzing the increasing data volumes that are, and will be, acquired. Here, we present CHIMERA 2.0 , an advanced computational framework for hierarchical Bayesian inference of cosmological, modified gravity, and population hyperparameters using standard sirens and galaxy catalogs. This upgrade introduces novel GPU-accelerated algorithms to estimate the hierarchical likelihood, enabling the analysis of thousands of events – crucial for next-generation experiments – and includes the two-parameter (Ξ 0 − n ) modified GW propagation model, where Ξ 0 governs the amplitude of the modification (Ξ 0 = 1 corresponds to GR). Using CHIMERA 2.0 , we forecast cosmological and modified GW propagation constraints for a scenario similar to the future LIGO-Virgo-KAGRA O5 run. We analyze three binary black-hole populations of 300 events at S/N > 20, each with a different value of Ξ 0 : 0.6, 1 (corresponding to GR), and 1.8. Multiple analyses were performed each catalog, comprising a population of approximately 5000 events, thanks to CHIMERA 2.0 , which is 10–1000 times faster depending on the settings and catalog size. We jointly infer cosmological, modified GW propagation, and population hyperparameters. With spectroscopic galaxy catalogs, the fiducial Ξ 0 is recovered with a precision of 22%, 7.5%, and 10% for Ξ 0 = 0.6, 1, and 1.8, respectively; while the precision on H 0 is 2 − 7 times worse than when Ξ 0 is not inferred. Finally, in the case of photometric redshifts the constraints degrade on average by 3.5 times in all cases, underscoring the importance of future spectroscopic surveys in maximizing the constraining power of standard sirens.

Gravitational waves were predicted by Albert Einstein more than a century ago, but only in 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) was able to detect them. The gravitational wave phenomenon can be compared to spreading water from a lake after a stone has been thrown into it. Here, gravitational wave generation comes from an astronomical binary system formed by black holes or neutron stars. However, unlike the water, the amplitude of those gravitational waves is on a scale smaller than a proton’s size. Despite this, we can describe it with simple equations in a phenomenological way. We can model those waves on a regular computer using post Newtonian physics. Here we were able to generate gravitational waves from computational simulations and make its data analyze. When a gravitational wave is detected in the real-world problem, there is a great interest in establishing the physical features of the astronomical bodies involved in the process. In this way, we propose applying a simple neural network to receive the gravitational wave data and infer information about the astronomical bodies’ mass. The experimental results show that a simple neural network can extract mass information from the gravitational wave data. The recognition process proposed is much more straightforward than the complex computation based on numerical relativity for gravitational wave data analysis.

With the recent claim that gravitational waves were finally detected and with other efforts around the world for GWs detection, its is reasonable to imagine that the relic gravitational wave background could be detected in some time in the future and with such information gather some hints about the origin of the universe. But, it’s also be considered that gravity has self-interaction, with such assumption it’s reasonable to expect that these gravitational wave will interact with the relic or nonrelic GW background by scattering, for example. Such interaction should decrease the distance which such propagating waves could be detected The propagation of gravitational waves (GWs) is analyzed in an asymptotically de Sitter space by the perturbation expansion around Minkowski space using a scalar component. Using the case of de Sitter inflationary phase scenario, the perturbation propagates through a FRW background. The GW, using the actual value for the Hubble scale (Ho), has a damping factor with a very small valor for the size of the observational universe; the stochastic relic GW background is given by a dimensionless function of the frequency. In this work we analyze this same damping including the gravitational wave background due to astrophysical sources such background is 3 orders of magnitude bigger in some frequencies and produces a higher damping factor.

We present a forecast for the upcoming Einstein Telescope (ET) interferometer with two new methods to infer cosmological parameters. We consider the emission of Gravitational Waves (GWs) from compact binary coalescences, whose electromagnetic counterpart is missing, namely Dark Sirens events. Most of the methods used to infer cosmological information from GW observations rely on the availability of a redshift measurement, usually obtained with the help of external data, such as galaxy catalogues used to identify the most likely galaxy to host the emission of the observed GWs. Instead, our approach is based only on the GW survey itself and exploits the information on the distance of the GW rather than on its redshift. Since a large dataset spanning the whole distance interval is expected to fully represent the distribution, we applied our methods to the expected ET's far-reaching measuring capabilities. We simulate a dataset of observations with ET using the package darksirens, assuming an underlying ΛCDM cosmology, and including the possibility to choose between three possible Star Formation Rate density (SFR) models, also accounting for possible population III stars (PopIII). We test two independent statistical methods: one based on a likelihood approach on the theoretical expectation of observed events, and another applying the cut-and-count method, a simpler method to compare the observed number of events with the predicted counts. Both methods are consistent in their final results, and also show the potential to distinguish an incorrect SFR model from the data, but not the presence of a possible PopIII. Concerning the cosmological parameters, we find instead that ET observations by themselves would suffer from strong degeneracies, but have the potential to significantly contribute to parameter estimation if used in synergy with other surveys.

The renewed global interest in lunar exploration, with multiple robotic and crewed landings planned in the coming decades, presents a unique opportunity to pursue scientific objectives that are difficult or infeasible on Earth. Among these objectives, the detection of gravitational waves (GWs) from a lunar platform stands out as a particularly promising frontier in fundamental physics. While Earth-based GW observatories have made groundbreaking discoveries, their sensitivity is fundamentally limited by environmental noise, including persistent seismic disturbances. In contrast, the Moon offers an exceptionally quiet seismic environment three orders of magnitude smaller than on Earth, which is largely free from atmospheric and anthropogenic noise sources, as originally demonstrated by data from the Apollo Passive Seismic Experiment.In this study, we revisit the Apollo-era seismic data to conduct a comprehensive assessment of the lunar seismic noise environment. Particularly, we revisit the transfer function of the Apollo instruments by using the existing catalog of the calibration signals. Using the newly developed transfer function (Specifically,) we perform a statistical analysis of background noise levels recorded at multiple Apollo seismic stations, characterizing the amplitude distribution, spectral content, and long-term variability of ambient seismic noise. Regional differences among the landing sites are examined to identify geophysical or environmental factors contributing to noise variability. We further analyze temporal trends in noise characteristics in relation to local time, surface temperature cycles, and tidal stresses, aiming to determine optimal observational windows for future ultra-sensitive measurements.In addition to persistent background noise, we assess the impact of transient seismic events, which may also pose challenges for GW detection. We compile and analyze the statistical properties, such as occurrence rates, amplitudes, and durations, of the three main classes of seismic events observed on the Moon: deep moonquakes, shallow moonquakes, and meteoroid impacts. Their respective contributions to the lunar seismic signal environment are evaluated, with particular attention to their potential to mask or mimic GW signals in the relevant frequency ranges. Here, careful consideration is given to the deep moonquakes, as their frequent seismic activity defines the seismic floor level for potential future GW detectors. We synthesize deep moonquake seismograms to construct a representative template of this signal class. These synthetic waveforms are then used to simulate the response of a prospective lunar strainmeter, allowing us to explore the signature of deep moonquake noise in a gravitational wave measurement context. We discuss the data analysis strategies developed to distinguish this seismic noise from a true GW signal in order to remove it, emphasizing the importance of signal discrimination methods in future lunar GW observatories.The results of our analysis provide updated and quantified constraints on the lunar seismic noise floor, as well as on the likelihood and characteristics of transient disturbances. These findings are essential for informing the design, site selection, and operational strategies of future lunar gravitational wave observatories. We conclude by discussing the implications of the current seismic environment for the detectability of various classes of GW sources, including low-frequency signals that may be inaccessible to Earth-based detectors.

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.

At the present, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant at the present era [1]–[2]. An important aspect to analyze is the propagation of gravitational waves and the screening or enhancement of the Newton constant GN in these models. The problem is that the Lorentz symmetry breaking terms may induce an unacceptable value of the Newton constant GN or introduce longitudinal modes in the gravitational wave propagation. Furthermore this breaking may spoil the standard dispersion relation ω=ck. In [3] the authors have presented a model suggesting that the behavior of the gravitational constant is correct for asymptotic times. In the present work, an explicit checking is made and we finally agree with these claims. Furthermore, it is suggested that the gravitational waves are also well behaved for large times. In the process, some new models with the same behavior are obtained, thus enlarging the list of possible adjustment mechanisms.