Propagation Of Gravitational Waves Research Articles

Propagation of anisotropic gravitational and electromagnetic waves at very high energies

We analyze the dispersion relation for an anisotropic gravity-electromagnetic theory at very high energies. In particular for photons of very high energy. We start by introducing the anisotropic gravity-gauge vector field model. It is invariant under spacelike diffeomorphisms, time parametrization, and U(1) gauge transformations. It includes high-order spacelike derivatives as well as polynomial expressions of the Riemann and field strength tensor fields. It is based on the Hořava-Lifshitz anisotropic proposal. We show its consistency, and the stability of the Minkowski ground state. Finally, we determine the exact zone at which the physical degrees of freedom, i.e. the transverse-traceless tensorial degrees of freedom and the transverse vectorial degrees of freedom propagate according to a linear wave equation. This is so, in spite of the fact that there exists in the zone a non-trivial Newtonian background of the same order. The wave equation contains spatial derivatives up to the sixth order, in the lowest order it exactly matches the relativistic wave equation. We then analyze the dispersion relation at very high energies in the context of recent experimental data. The qualitative predictions of the proposed model, concerning the propagation of highly energetic photons, are different from the ones obtained from the modified dispersion relation of the LIV models.

Scalar polarization window in gravitational-wave signals

Abstract Scalar polarization modes of gravitational waves, which are often introduced in the context of the viable extension of gravity, have been actively searched for. However, couplings of the scalar modes to matter are strongly constrained by fifth-force experiments. Thus, the amplitude of scalar polarization in the observed gravitational-wave signal must be significantly suppressed compared to that of the tensor modes. Here, we discuss the implications of the experiments in the solar system on the detectability of scalar modes in gravitational waves from compact binary coalescences, taking into account the whole processes from the generation to the observation of gravitational waves. We first claim that the energy carried by the scalar modes at the generation is, at most, that of the tensor modes from the observed phase evolution of the inspiral gravitational waves. Next, we formulate general gravitational-wave propagation and point out that the energy flux hardly changes through propagation as long as the background changes slowly compared to the wavelength of the propagating waves. Finally, we show that the possible magnitude of scalar polarization modes detected by ground-based gravitational-wave telescopes is already severely constrained by the existing gravity tests in the solar system.

Polar gravitational waves in f(R, T ϕ ) framework

This work analyzes the propagation of polar gravitational waves for flat FRW cosmic background and in view of f(R, T ϕ ) theory. In what follows, we opt for the Regge-Wheeler polar perturbation scheme in flat geometry of background spacetime and corresponding scalar, field source is also perturbed. The two sets of field equations for flat and perturbed geometry are constructed and furthermore used to evaluate perturbation parameters. The obtained expressions suggest that polar fluctuations affect both geometry and scalar field. The radial and temporal parts of perturbation parameters χ and σ are plotted explicitly while the behavior of ψ is observed via a numerical solution plotted as a 3D graph. The change in these fluctuations for different values of model parameter λ is noticed through these plots.

Mirage of Luminal Modified Gravitational-Wave Propagation.

Using conformal invariance of gravitational waves, we show that for a luminal modified gravity theory, the gravitational-wave propagation and luminosity distance are the same as in general relativity. The relation between the gravitational-wave and electromagnetic-wave luminosity distance gets modified, however, for electromagnetism minimally coupled to the Jordan frame metric. Using effective field theory we show that the modified relation obtained for luminal theories is also valid for nonluminal theories with Jordan frame matter-gravity coupling. We generalize our analysis to a time-dependent speed of gravitational waves with matter minimally coupled to either the Jordan or Einstein frame metrics.

Gravitational versus Magnetohydrodynamic Waves in Curved Spacetime in the Presence of Large-Scale Magnetic Fields

The general-relativistic (GR) magnetohydrodynamic (MHD) equations for a conductive plasma fluid are derived and discussed in the curved spacetime described by Thorne’s metric tensor, i.e., a family of cosmological models with inherent anisotropy due to the existence of an ambient, large-scale magnetic field. In this framework, it is examined whether the magnetized plasma fluid that drives the evolution of such a model can be subsequently excited by a transient, plane-polarized gravitational wave (GW) or not. To do so, we consider the associated set of the perturbed equations of motion and integrate them numerically in order to study the evolution of instabilities triggered by the GW propagation. In particular, we examine to what extend perturbations of the electric and/or the magnetic field can be amplified due to a potential energy transfer from the GW to the electromagnetic (EM) degrees of freedom. The evolution of the perturbed quantities depends on four free parameters, namely, the conductivity of the fluid, σ; the speed of sound square, 13<Csc2≡γ<1, which in this model may serve also as a measure of the inherent anisotropy; the GW frequency, ωg; and the associated angle of propagation with respect to the direction of the magnetic field, θ. We find that GW propagation in the anisotropic magnetized medium under consideration does excite several MHD modes; in other words, there is energy transfer from the gravitational to the EM degrees of freedom that can result in the acceleration of charged particles at the spot and in the subsequent damping of the GW.

Modified propagation of gravitational waves from the early radiation era

We study the propagation of cosmological gravitational wave (GW) backgrounds from the early radiation era until the present day in modified theories of gravity. Comparing to general relativity (GR), we study the effects that modified gravity parameters, such as the GW friction α M and the tensor speed excess α T, have on the present-day GW spectrum. We use both the WKB estimate, which provides an analytical description but fails at superhorizon scales, and numerical simulations that allow us to go beyond the WKB approximation. We show that a constant α T makes relatively insignificant changes to the GR solution, especially taking into account the constraints on its value from GW observations by the LIGO-Virgo collaboration, while α M can introduce modifications to the spectral slopes of the GW energy spectrum in the low-frequency regime depending on the considered time evolution of α M. The latter effect is additional to the damping or growth occurring equally at all scales that can be predicted by the WKB approximation. In light of the recent observations by pulsar timing array (PTA) collaborations, and the potential observations by future detectors such as SKA, LISA, DECIGO, BBO, or ET, we show that, in most of the cases, constraints cannot be placed on the effects of α M and the initial GW energy density ℰ* GW separately, but only on the combined effects of the two, unless the signal is observed at different frequency ranges. In particular, we provide some constraints on the combined effects from the reported PTA observations.

Viscous attenuation of gravitational waves propagating through an inhomogeneous background

We consider the propagation of gravitational waves in the late-time Universe in the presence of matter distribution inhomogeneities, and we also consider the cosmic fluid to be viscous. In this work, we investigate the cumulative effect of inhomogeneities and viscosity of the cosmic-fluid on the observables associated with the sources of the gravitational waves. Employing Buchert’s averaging procedure in the backreaction framework, we consider a model of spacetime in which matter is distributed in-homogeneously across space. Using the modified redshift versus distance relation, through the averaging process in the context of the model, we study the variation of the redshift-dependent part of the observed gravitational wave amplitude for different combinations of our model parameters while simultaneously considering damping of the gravitational wave amplitude due to viscosity of the cosmic-fluid. Then, we investigate the differences occurring in the variation of the redshift-dependent part of the observed gravitational wave amplitude due to consideration of viscous attenuation. We show that there are significant deviations after the inclusion of viscous attenuation in our analysis, depending on the chosen value of the coefficient of viscosity. Our result signifies the importance of the effect of viscosity, within the model of an inhomogeneous Universe, on precision measurements of parameters of compact-binary sources of gravitational waves.

Chiral gravitational waves in Palatini-Chern-Simons gravity

We study the parity-breaking higher-curvature gravity theory of Chern-Simons (CS), using the Palatini formulation in which the metric and connection are taken to be independent fields. We first show that Palatini-CS gravity leads to first-order derivative equations of motion and thus avoid the typical instabilities of CS gravity in the metric formalism. As an initial application, we analyze the cosmological propagation of gravitational waves (GWs) in Palatini-CS gravity. We show that, due to parity breaking, the polarizations of GWs suffer two effects during propagation: amplitude birefringence (which changes the polarization ellipticity) and velocity birefringence (which rotates the polarization plane). While amplitude birefringence is known to be present in CS gravity in the metric formalism, velocity birefringence is not present in metric CS gravity for high frequency waves, but now appears in Palatini-CS due to the fact that left-handed and right-handed GW polarizations have a different dispersion relation. In the approximation of small deviations from general relativity (GR), we do find however that velocity birefringence appears at least quadratically in the CS coupling parameter $\ensuremath{\alpha}$, while amplitude birefringence appears linearly in $\ensuremath{\alpha}$. This means that amplitude birefringence will be the most relevant effect in Palatini-CS and hence this model will behave similarly to metric CS. We confirm this by applying current constraints on amplitude and velocity birefringence to Palatini-CS, and showing that those from amplitude birefringence give the tightest bounds.

Testing gravity with gravitational wave friction and gravitational slip

Gravitational waves (GWs) emitted by binary sources are interesting signals for testing gravity on cosmological scales since they allow measurements of the luminosity distance. When followed by electromagnetic counterparts, in particular, they enable a reconstruction of the GW-distance-redshift relation. In the context of several modified gravity (MG) theories, even when requiring that the speed of propagation is equal to that of light, this GW distance differs from the standard electromagnetic luminosity distance due to the presence of a modified friction in the GW propagation. The very same source of this friction, which is the running of an effective Planck mass, also affects the scalar sector generating gravitational slip, i.e. a difference between the scalar potentials, an observable that can be inferred from large-scale structure (LSS) probes. In this work, we use a model within effective field theories for dark energy to exemplify precisely the fact that, at the linear perturbation level, parametrizing a single function is already enough to generate simultaneous deviations in the GW distance and the slip. By simulating multimessenger GW events that might be detected by the Einstein Telescope in the future, we compare the constraining power of the two observables on this single degree of freedom. We then combine forecasts of an Euclid-like survey with GW simulations, coming to the conclusion that, when using Planck data to better constrain the cosmological parameters, those future data on the scalar and tensor sectors are competitive to probe such deviations from General Relativity, with LSS giving stronger (but more model-dependent) results than GWs.

Non canonical polarizations of gravitational waves

We hereby propose an alternative and additional angle on the nature of gravitational waves (GWs), postulating the theoretical and experimental possibility that GWs carry a deformation of the time component of spacetime, other than the spatial one. By explicitly working outside of the transverse-traceless gauge, we propose how events with well-defined time duration, when hit by a GW, would consequently be expected to show a difference in their characteristic time, as measured from the rest frame of an outside observer, whose clock is to remain unaffected by the GW. This constitutes a theoretically viable way in the sense of detecting the passing of the wave itself and may prove relevant as a standalone method for GWs detection other than laser interferometers, or as well be implemented as a complementary but independent system of signal triggering, improving the statistical significance of existing methods. A simple but physically realistic scenario in which the appropriate conditions for the generation and detection of GWs with time dilation are met is presented, along with the conceptual design of an experimental detector.

Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory

We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these equations to the study of cosmological solutions of the Einstein-Cartan theory in which the matter is modeled by a perfect fluid with intrinsic spin. It is shown that the metric tensor can be described by a generic FLRW solution. However, due to the presence of torsion the Weyl tensors might not vanish. The coupling between the torsion and Weyl tensors leads to the conclusion that, in this cosmological model, the universe must either be flat or open, excluding definitely the possibility of a closed universe. In the open case, we derive a wave equation for the traceless part of the magnetic part of the Weyl tensor and show how the intrinsic spin of matter in a dynamic universe leads to the generation and emission of gravitational waves. Lastly, in this cosmological model, it is found that the torsion tensor, which has an intrinsic spin as its source, contributes to a positive accelerated expansion of the universe. Comparing the theoretical predictions of the model with the current experimental data, we conclude that torsion cannot completely replace the role of a cosmological constant.

Gravitational waveform and polarizationfrom binary black hole inspiral in dynamical Chern-Simons gravity: from generation to propagation

We calculate the gravitational waveform radiated from spinning black holes (BHs) binary in dynamical Chern-Simons (dCS) gravity. The equation of motion (EOM) of the spinning binary BHs is derived based on the modified Mathisson-Papapetrou-Dixon equation for the spin-aligned circular orbits. The leading-order effects induced by the dCS theory contain spin-spin interaction and monopole-quadrupole interaction, which influences both the EOM of the binary system and corresponding gravitational waveform at the second post-Newtonian (PN) order (i.e., 2PN order). After reporting the waveforms, we investigate the polarization modes of gravitational waves (GWs) in dCS theory. None of the extra modes appears in this theory up to the considered PN order. Moreover, since the time scale of the binary merger is much smaller than that of the cosmological expansion, the parity-violating effect of the dCS theory does not appear in the process of GW generation. However, during the process of GW propagation, amplitude birefringence, a typical parity-violating effect, makes plus and cross modes convert to each other, which modifies the gravitational waveform at 1.5PN order.

Collapsing cylindrically symmetric filamentary stellar object

This work investigates the collapsing behavior of filamentary objects under the influence of dark matter. For this purpose, we use f(R, T) gravity as a candidate for dark matter. The collapse equation is obtained by imposing the Darmois junction condition at the collapsing boundary. At the collapsing boundary, it is observed that the radial pressure is non-zero and is proportional to the field time-dependent component. Finally, we check the relationship between gravitational waves and dark source terms. It is concluded that the dark source terms disrupt the propagation of gravitational waves.

Black Hole Formation and Gravitational Waves Generation

In the present day, black holes have recently attracted a variety of attention. Black holes and gravitational waves were studied more than 100 years ago. From theoretical reasoning and formula derivation to detector observation, people never stop to explore these curious things. This paper mainly describes the essential information and principle of black holes, and gravitational waves, as well as the basic operation principle of LIGO detectors. The basic definition of gravitational wave and several sources of the gravitational wave is discussed in this paper. According to the analysis, the properties of waves can be used in detecting gravitational waves, as well as more hidden matter. In 1915, Einstein proposed the general theory of relativity, which foresaw the existence of black holes but did not believe that black holes were real. In the 1960s, American scientist John Wheeler first named this incredible celestial body black hole. The search for gravitational waves has had a profound impact on people. With gravitational waves, people can discover an unknown matter which can be studied and benefit humankind. These results shed light on guiding further exploration of dark energy, matters, and more black hole observations.

Search for anisotropic, birefringent spacetime-symmetry breaking in gravitational wave propagation from GWTC-3

An effective field theory framework, the Standard-Model Extension, is used to investigate the existence of Lorentz and CPT-violating effects during gravitational wave propagation. We implement a modified equation for the dispersion of gravitational waves, that includes isotropic, anisotropic and birefringent dispersion. Using the LIGO-Virgo-KAGRA algorithm library suite, we perform a joint Bayesian inference of the source parameters and coefficients for spacetime symmetry breaking. From a sample of 45 high confidence events selected in the GWTC-3 catalog, we obtain a maximal bound of $3.19 \times 10^{-15}$~m at 90\% CI for the isotropic coefficient $k_{(V)00}^{(5)}$ when assuming the anisotropic coefficients to be zero. The combined measurement of all the dispersion parameters yields limits on the order of $10^{-13}$~m for the 16 $k_{(V)ij}^{(5)}$ coefficients. We study the robustness of our inference by comparing the constraints obtained with different waveform models, and find that a lack of physics in the simulated waveform may appear as spacetime symmetry breaking-induced dispersion for a subset of events.

Propagation of scalar and tensor gravitational waves in Horndeski theory

Gravitational waves travel through the distributions of matter and dark energy during propagation. For this reason, gravitational waves emitted from binary compact objects serve as a useful tool especially to probe the nature of dark energy. The geometrical optics approximation is a conventional way of investigating wave propagation. However, the approximation becomes less accurate as the wavelength approaches the curvature radius of the background, which can occur in generic situations. In this paper, we suggest a formulation for higher-order corrections of the geometrical optics expansion, applied to Horndeski theory which accommodates many dark energy models. At the level of the background, assuming that the derivative of the scalar field is non-vanishing and timelike, we choose the time slices to coincide with the contours of the scalar field. This choice of the background time slices is advantageous as the sound cones of both scalar and tensor gravitational waves are upright with respect to the background time slices whenever the scalar field behaves as a perfect fluid. We then analyze the equations of motion for scalar and tensor components of gravitational waves at the leading and next-to-leading order in the geometrical optics expansion, deriving the evolution equations for their amplitudes under certain conditions. In particular, for Generalized Brans-Dicke theories, we find a simple description of equations for gravitational waves in terms of an effective metric.

Prospects of probing dark matter condensates with gravitational waves

The Lambda-Cold Dark Matter model explains cosmological observations most accurately till date. However, it is still plagued with various shortcomings at galactic scales. Models of dark matter such as superfluid dark matter, Bose-Einstein Condensate(BEC) dark matter and fuzzy dark matter have been proposed to overcome some of these drawbacks. In this work, we probe these models using the current constraint on the gravitational wave (GW) propagation speed coming from the binary neutron star GW170817 detection by LIGO-Virgo detector network and use it to study the allowed parameter space for these three models for Advanced LIGO+Virgo, LISA, IPTA and SKA detection frequencies. The speed of GW has been shown to depend upon the refractive index of the medium, which in turn, depends on the dark matter model parameters through the density profile of the galactic halo. We constrain the parameter space for these models using the bounds coming from GW speed measurement and the Milky Way radius bound. Our findings suggest that with Advanced LIGO-Virgo detector sensitivity, the three models considered here remain unconstrained. A meaningful constraint can only be obtained for detection frequencies ≤ 10-9 Hz, which falls in the detection range of radio telescopes such as IPTA and SKA. Considering this best possible case, we find that out of the three condensate models, the fuzzy dark matter model is the most feasible scenario to be falsified/validated in near future.

Testing gravitational wave propagation with multiband detections

Effective field theories (EFT) of dark energy (DE) — built to parameterise the properties of DE in an agnostic manner — are severely constrained by measurements of the propagation speed of gravitational waves (GW). However, GW frequencies probed by ground-based interferometers lie around the typical strong coupling scale of the EFT, and it is likely that the effective description breaks down before even reaching that scale. We discuss how this leaves the possibility that an appropriate ultraviolet completion of DE scenarios, valid at scales beyond an EFT description, can avoid present constraints on the GW speed. Instead, additional constraints in the lower frequency LISA band would be harder to escape, since the energies involved are orders of magnitude lower. By implementing a method based on GW multiband detections, we show indeed that a single joint observation of a GW150914-like event by LISA and a terrestrial interferometer would allow one to constrain the speed of light and gravitons to match to within 10-15. Multiband GW observations can therefore firmly constrain scenarios based on the EFT of DE, in a robust and unambiguous way.

Parameter estimation of eccentric gravitational waves with a decihertz observatory and its cosmological implications

Eccentricity of compact binaries can improve the parameter estimation of gravitational waves (GWs), which is due to the fact that the multiple harmonics induced by eccentricity can provide more information and break the degeneracy between waveform parameters. In this paper, we first investigate the parameter estimation of eccentric GWs with decihertz observatory. We consider two scenarios for the configuration of DECIGO, i.e., the one cluster of DECIGO with its design sensitivity and B-DECIGO which also has one cluster but with inferior sensitivity as a comparison. We adopt the Fisher matrix to estimate the parameter errors. By mocking up the typical binaries in GWTC-3, we find a nonvanishing eccentricity can significantly improve the estimation for almost all waveform parameters. In particular, the localization of typical binary black holes (BBH) can achieve $\mathcal{O}(10--{10}^{3.5})$ factors of improvement when the initial eccentricity ${e}_{0}=0.4$ at 0.1 Hz. The precise localization of binary neutron stars (BNS) and neutron star--black hole binaries (NSBH), together with the large improvement of localization of BBH from eccentricity in the midband, inspire us to construct the catalogs of golden dark sirens whose host galaxies can be uniquely identified. We find that with only one cluster of DECIGO running 1 year in its design sensitivity, hundreds of golden dark BNS, NSBH, and tens of golden dark BBH can be observed. Eccentricity can greatly increase the population of golden dark BBH from $\ensuremath{\sim}7({e}_{0}=0)$ to $\ensuremath{\sim}65({e}_{0}=0.2)$. Such an increase of population of golden dark BBH events can improve the precision of Hubble constant measurement from 2.06% to 0.68%, matter density parameter from 64% to 16% in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. Through the phenomenological parametrization of GW propagation, the constraints of modified gravity can be improved from 6.2% to 1.6%. Our results show the remarkable significance of eccentricity for the detection and parameter estimation of GW events, allowing us to probe the Universe precisely.

Gravitational wave constraints on spatial covariant gravities

The direct discovery of gravitational waves (GWs) from the coalescence of compact binary components by the LIGO/Virgo/KAGRA Collaboration provides an unprecedented opportunity for exploring the underlying theory of gravity that drives the coalescence process in the strong and highly dynamical field regime of gravity. In this paper, we consider the observational effects of spatial covariant gravities on the propagation of GWs in the cosmological background and obtain the observational constraints on coupling coefficients in the action of spatial covariant gravities from GW observations. We first decompose the GWs into the left- and right-hand circular polarization modes and derive the effects of the spatial covariant gravities on the propagation equation of GWs. We find that these effects can be divided into three classes: 1) frequency-independent effects on GW speed and friction, 2) parity-violating amplitude and velocity birefringences, and 3) a Lorentz-violating damping rate and dispersion of GWs. With these effects, we calculate the corresponding modified waveform of GWs generated by the coalescence of compact binaries. By comparing these new effects with the publicly available posterior samples or results from various tests of gravities with LIGO/Virgo/KAGRA data in the literature, we derive the observational constraints on coupling coefficients of the spatial covariant gravities. These results represent the most comprehensive constraints on the spatial covariant gravities in the literature.