Speed Of Gravitational Waves Research Articles

Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields

In this paper, we investigate the time dependent black holes in the frame of Einstein–Gauss–Bonnet theory having two scalar fields and investigate the propagation of the gravitational wave (GW). In the reconstructed models, there often appear ghosts, which could be eliminated by imposing some constraints. We investigate the behavior of high-frequency gravitational waves by examining the effects of varying Gauss–Bonnet coupling during their propagation. The speed of propagation changes due to the coupling during the black hole formation process. The propagation speed of gravitational waves differs when they enter the black hole compared to when they exit.

Probing the speed of scalar induced gravitational waves from observations

The propagation speed of gravitational waves is a fundamental issue in gravitational theory. According to general relativity, gravitational waves propagate at the speed of light. However, alternative theories of gravity propose modifications to general relativity, including variations in the speed of gravitational waves. In this paper, we investigate scalar-induced gravitational waves that propagate at speeds different from the speed of light. First, we analytically calculate the power spectrum of scalar induced gravitational waves based on the speed and spectrum of primordial curvature perturbations. We then explore several scalar power spectra, deriving corresponding fractional energy densities, including monochromatic spectrum, scale-invariant spectrum, and power-law spectrum. Finally, we constrain scalar-induced gravitational waves and evaluate the signatures of their speed from the combination of CMB+BAO and gravitational wave observations. Our numerical results clearly illustrate the influence of the speed of scalar-induced gravitational waves.

Dark energy with a shift-symmetric scalar field: Obstacles, loophole hunting and dead ends

We discuss the possibility of a scalar field being the fundamental description of dark energy. We focus on shift-symmetric scalar-tensor theories since this symmetry potentially avoids some fine-tuning problems. We also restrict attention to theories satisfying that the propagation speed of gravitational waves is equal to the speed of light. These considerations lead us to investigate shift-symmetric Kinetic Gravity Braiding theories. Analysing the stability of scalar linear perturbations, we discuss the conditions that seems to be necessary to describe (super) accelerated cosmic expansion without introducing instabilities. However, it has been previously established that the linearised analysis does not guarantee the stability of this non-canonical scalar theory, as potentially dangerous interactions between dark energy fluctuations and tensor perturbations (essentially gravitational waves) appear at a higher order in perturbation theory. Indeed, although we shall point out that the standard proof of absence of dark energy stable braiding models due to this interaction has a possible way-out, we find general arguments suggesting that there are no dark energy stable solutions that can exploit this loophole. Thus, we discuss future research directions for finding viable fundamental descriptions of dark energy. We also provide a dictionary between the covariant version of the theory and that of the Effective Field Theory approach, explicitly computing the parameters in the latter formalism in terms of the functions appearing in the covariant version, and its derivatives. To the best of our knowledge, this is the first time these expressions are explicitly obtained up-to arbitrary order in perturbation theory.

Early dark energy and scalarization in a scalar-tensor model

We present a model in which the Gauss-Bonnet invariant holds the quintessence at a fixed point, respecting an initial Z2 symmetry in the radiation-dominated era. This results in an early dark energy that becomes significant around the matter-radiation equality era. However, due to Z2 symmetry breaking, scalarization occurs, leading to a rapid reduction in the early dark energy density. The model then quickly behaves like the ΛCDM model. This scenario may also explain the reduction of sound horizon and aligns with the assumption that the gravitational wave speed is infinitesimally close to the speed of light.

Phenomenology of Horndeski gravity under positivity bounds

A set of conditions that any effective field theory needs to satisfy in order to allow for the existence of a viable UV completion, has recently gained attention in the cosmological context under the name of positivity bounds. In this paper we revisit the derivation of such bounds for Horndeski gravity, highlighting the limitations that come from applying the traditional methodology to a theory of gravity on a cosmological background. We then translate these bounds into a complete set of viability conditions in the language of effective field theory of dark energy. We implement the latter into EFTCAMB and explore the large scale structure phenomenology of Horndeski gravity under positivity bounds. We build a statistically significant sample of viable Horndeski models, and derive the corresponding predictions for the background evolution, in terms of w DE, and the dynamics of linear perturbations, in terms of the phenomenological functions μ and Σ, associated to clustering and weak lensing, respectively. We find that the addition of positivity bounds to the traditional no-ghost and no-gradient conditions considerably tightens the theoretical constraints on all these functions. The most significant feature is a strengthening of the correlation μ ≃ Σ, and a related tight constraint on the luminal speed of gravitational waves c 2 T ≃ 1. In this work we demonstrate the strong potential of positivity bounds in shaping the viable parameter space of scalar-tensor theories. This is certainly promising, but it also highlights the importance of overcoming all issues that still plague a rigorous formulation of the positivity bounds in the cosmological context.

Horndeski-like gravity perturbation induced by large-magnitude earthquake

We hypothesis that large earthquakes generate Horndeski-like Gravitational Wave (GW). We find that such a Horndeski-like GW propagates with the speed of sound. The sound waves generated by an earthquake make a local and temporal change to the Earth’s diagravitational medium; therefore, they modify the GW speed in a standard, Alternative-Theory-of-Gravity (ATG) sense. The quantum of the Horndeski-like GW is a massless scalar quasiparticle and cannot exist outside of the propagation region of the P-field. The Horndeski-like GW may be detectable by future GW detectors with a sensitivity of 10–15 Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Hz}^{{-1/2}}$$\\end{document} in the region of 0.1–1 Hz.

Simulation Study on Constraining Gravitational Wave Propagation Speed by Gravitational Wave and Gamma-ray Burst Joint Observation on Binary Neutron Star Mergers

Theories of modified gravity suggest that the propagation speed of gravitational waves (GW) v g may deviate from the speed of light c. A constraint can be placed on the difference between c and v g with a simple method that uses the arrival time delay between GW and electromagnetic wave simultaneously emitted from a burst event. We simulated the joint observation of GW and short gamma-ray burst signals from binary neutron star merger events in different observation campaigns, involving advanced LIGO (aLIGO) in design sensitivity and Einstein Telescope (ET) joint-detected with Fermi/GBM. As a result, the relative precision of constraint on v g can reach ∼10−17 (aLIGO) and ∼10−18 (ET), which are one and two orders of magnitude better than that from GW170817, respectively. We continue to obtain the bound of graviton mass m g ≤ 7.1(3.2) × 10−20 eV with aLIGO (ET). Applying the Standard-Model Extension test framework, the constraint on v g allows us to study the Lorentz violation in the nondispersive, nonbirefringent limit of the gravitational sector. We obtain the constraints of the dimensionless isotropic coefficients s¯00(4) at mass dimension d = 4, which are −1×10−15<s¯00(4)<9×10−17 for aLIGO and −4×10−16<s¯00(4)<8×10−18 for ET.

Revisiting Einstein-Gauss-Bonnet theories after GW170817

In this work we study the inflationary framework of Einstein-Gauss-Bonnet theories which produce a primordial gravitational wave speed that respects the constraint imposed by the GW170817 event, namely |cT2−1|<6×10−15 in natural units. For these theories in general, the scalar Gauss-Bonnet coupling function ξ(ϕ) is arbitrary and unrelated to the scalar potential. We develop the inflationary formalism of this theory, and present analytic forms for the slow-roll indices, the observational indices and the e-foldings number, assuming solely a slow-roll era and also that the constraints imposed by the GW170817 event hold true. We present in detail an interesting class of models that produces a viable inflationary era. Finally, we investigate the behavior of the Einstein-Gauss-Bonnet coupling function during the reheating era, in which case the evolution of the Hubble rate satisfies a constant-roll-like relation H˙=δH2. As we show, the behavior of the scalar Gauss-Bonnet coupling during the reheating is different from that of the inflationary era. This is due to the fact that the evolution governing the reheating is different compared to the inflationary era.

Probing the speed of scalar-induced gravitational waves with pulsar timing arrays

Probing the speed of scalar-induced gravitational waves with pulsar timing arrays

Correlations for an anisotropic polarized stochastic gravitational wave background in pulsar timing arrays

The recent compelling observation of the nanohertz stochastic gravitational wave background has brought to light a new galactic arena to test gravity. In this paper, we derive a formula for the most general expression of the stochastic gravitational wave background correlation that could be tested with pulsar timing and future square kilometer arrays. Our expressions extend the harmonic space analysis, also often referred to as the power spectrum approach, to predict the correlation signatures of an anisotropic polarized stochastic gravitational wave background with subluminal tensor, vector, and scalar gravitational degrees of freedom. We present the first few nontrivial anisotropy and polarization signatures in the correlation and discuss their dependence on the gravitational wave speed and pulsar distances. Our results set up tests that could potentially be used to rigorously examine the isotropy of the stochastic gravitational wave background and strengthen the existing constraints on possible non-Einsteinian polarizations in the nanohertz gravitational wave regime.

Effective speed of gravitational waves

We derive an effective equation and action for the propagation of gravitational waves (GW), encoding the effects of interaction and self-interaction in a time, frequency and polarization dependent effective speed. In terms of an appropriately defined effective metric, the effective action takes the form a massless Klein-Gordon action.This effective approach predicts that for theories with matter coupled to the Einstein frame metric the ratio between gravitational and electromagnetic (EM) luminosity distance depends on the effective speed, while for Jordan frame matter coupling it depends on the effective Planck mass. We discuss how the frequency and polarization dependence of the GW-EM distance ratio provides a new test of general relativity and its modifications, and more in general of the interaction of GWs with other fields.

Probing the speed of gravitational waves beyond general relativity from CMB observations

In modified gravity theories, gravitational waves can propagate differently from general relativity and their propagating speed can be either constant or acquire a time dependence. We consider the constant models first and update the constraints on cosmological parameters from the combinations of [Formula: see text] datasets. In this case, excluding superluminal propagation, we obtain the lower limit on the speed [Formula: see text] at 95% C.L. A non-trivial propagating speed impacts the amplitude of tensor spectrum by adding a factor [Formula: see text], where [Formula: see text] is the tensor tilt. We find that the value of [Formula: see text] has positive correlation with the tensor-to-scalar ratio and anti-correlation with the factor [Formula: see text]. Then we explore a time-dependent speed which contains the resonance of the stochastic gravitational wave background. If the speed of gravitational waves oscillates at primordial era, resonance continuously enhances stochastic gravitational wave background which produces observable effects on tensor power spectra. We derive the constraints on the amplitude of oscillatory speed and tensor parameters from the combinations of [Formula: see text] datasets. The numerical results show that the speed resonance of the stochastic gravitational wave background is sensitive to CMB observations.

Scalar-Gauss-Bonnet model, the coincidence problem and the gravitational wave speed

We introduce a dynamical dark energy model wherein quintessence interacts with both the Gauss-Bonnet invariant and dark matter. Initially, the Gauss-Bonnet invariant stabilizes the quintessence at a fixed point, resulting in a negligible density of dark energy. Subsequently, the conformal coupling to dark matter triggers the evolution of dark energy. This model proposes an explanation for the initial absence of dark energy in radiation era and its later emergence during the matter-dominated era, achieving a magnitude comparable to dark matter in the present epoch. In this scenario, the Gauss-Bonnet term does not directly influence late-time cosmic evolution. Our model aligns with the assumption that the speed of gravitational wave is infinitesimally close to the speed of light.

Quintessence in the Weyl-Gauss-Bonnet model

Quintessence models have been widely examined in the context of scalar-Gauss-Bonnet gravity, a subclass of Horndeski's theory, and were proposed as viable candidates for Dark Energy. However, the relatively recent observational constraints on the speed of gravitational waves c GW have resulted in many of those models being ruled out because they predict c GW ≠ c generally. While these were formulated in the metric formalism of gravity, we put forward a new quintessence model with the scalar-Gauss-Bonnet action but in Weyl geometry, where the connection is not metric compatible. We find the fixed points of the dynamical system under some assumptions and determine their stability via linear analysis. The past evolution of the Universe can be reproduced correctly, but the late Universe constraints on c GW are grossly violated. Moreover, at these later stages tensor modes suffer from the gradient instabilities. We also consider the implications of imposing an additional constraint c GW = c, but this does not lead to evolution that is consistent with cosmological observations.

Gravitational waves on charged black hole backgrounds in modified gravity

The stability of Reissner–Nördstrom black holes with an extremal mass–charge relation was determined by calculating the propagation speed of gravitational waves on this background in an effective field theory (EFT) of gravity. New results for metric components are shown, along with the corresponding new extremal relation, part of which differs by a global factor of 2 from the past published work. This new relation further develops the existing constraints on EFT parameters. The radial propagation speed for gravitational waves in the Regge–Wheeler gauge was calculated linearly for all perturbations, yielding exact luminality for all dimension-4 operators. The dimension-6 radial speed modifications introduce no constraints on the sign of the modified theory parameters from causality arguments, while the deviation from classical theories vanishes at both horizons. The angular speed was found to be altered for the dimension-4 operators, with possible new constraints on the modified theory being suggested from causality arguments. Results are consistent with existing literature on Schwarzschild black hole backgrounds, with some EFT terms becoming active only in non-vacuum spacetimes such as Reissner–Nördstrom black holes.

Propagation speed of gravitational wave in scalar–Einstein–Gauss-Bonnet gravity

The propagation speed of the gravitational wave in scalar–Einstein–Gauss-Bonnet (sEGB) gravity is generally different from that of light. Using differential equation conditions for the speed of gravitational waves to coincide with the light speed in the expanding universe, we constructed a general class of sEGB gravities where this condition is satisfied and realistic inflation occurs. It is demonstrated that the condition that the speed of gravitational wave coincides with that of the light in the Friedmann-Lemaître-Robertson-Walker (FRLW) universe is always different from the condition for gravitational wave speed in the sEGB black hole background. Moreover, it is shown that when gravitational wave speed in sEGB black hole is equal to the speed of light the black hole spacetime geometry is changing too so that formally there is no solution for such sEGB black hole. This may indicate that sEGB black holes hardly can be considered as realistic black holes unless some reasonable scenario to make gravitational wave speed to be equal to that of light is proposed, at least asymptotically.

Does the speed of gravitational waves depend on the source velocity?

Does the speed of gravitational waves depend on the source velocity?

Gauss-Bonnet Dark Energy and the speed of gravitational waves

Gauss-Bonnet Dark Energy has been a popular model to explainthe accelerated expansion of the Universe. Quite generically it alsopredicts the speed of gravitational waves c GW to be differentfrom the speed of light. This fact alone led some authors to excludesuch models in view of the new tight observational constraints on c GW. However, the behaviour of c GW depends on the choice ofthe Gauss-Bonnet (GB) coupling function. It is possible to constructmodels where c GW is always equal to the speed of light. More generally, c GW is a time dependent function with instances where both speedscoincide. Nevertheless, we observe that the bound on c GW excludesscenarios where the GB term directly affects the expansion of theUniverse, even if the constraint on the variation of the couplingfunction does not appear to be strong. We perform the dynamical systemsanalysis to see if the expansion of the Universe could be affectedindirectly by modulating the behaviour of the scalar field, whichmodulates the GB coupling. It is shown that either the bounds on c GWare violated by many orders of magnitude, or it might be very difficultto find models that are consistent with other cosmological observations.

Inflation using a triplet of antisymmetric tensor fields

We study an inflation model driven by a triplet of antisymmetric tensor fields, with minimal and nonminimal couplings to gravity. First, we show that the presence of a triplet of antisymmetric tensor fields can provide inherent background isotropy in the stress–energy tensor contrary to the past studies using an antisymmetric tensor field. Inflation is supported in the presence of non-minimal couplings with gravity. We perform the slow roll analysis and also analyse perturbations to the antisymmetric tensor field as well as the tensor modes of perturbed metric. The speed of gravitational waves manifested from the tensor perturbations is tuned to c. We also study the evolution of the gravitational waves, calculate their power spectrum and tensor spectral index.

Constraining Palatini–Horndeski theory with gravitational waves after GW170817

In this paper, we investigate the possible parameter space of Palatini–Horndeski theory with gravitational waves in a spatially flat Universe. We develop a general method for obtaining the speed of gravitational waves in the Palatini formalism in the cosmological background and we find that if the theory satisfies the following condition: in any spatially flat cosmological background, the tensor gravitational wave speed is the speed of light c, then only S = int d^4x sqrt{-g} big [K(phi ,X)-G_{3}(phi ,X){{tilde{Box }}}phi +G_{4}(phi ){tilde{R}}big ] is left as the possible action in Palatini–Horndeski theory. We also find that when G_{5}(phi ,X)ne 0, the tensor part of the connection will propagate and there are two different tensor gravitational wave speeds.