Propagation Speed Of Gravitational Waves Research Articles

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.

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.

Measuring the propagation speed of gravitational waves with LISA

The propagation speed of gravitational waves, cT , has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent cT . Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of cT from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ansätze for cT (f), and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on cT (f) obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart.

Cosmic evolution in DHOST theory with scaling solutions

We study cosmic evolution based on the fixed points in the dynamical analysis of the degenerate higher-order scalar-tensor (DHOST) theories. We consider the DHOST theory in which the propagation speed of gravitational waves is equal to the speed of light, the tensor perturbations do not decay to dark energy perturbations, and the scaling solutions exist. The scaling fixed point associated with late-time acceleration of the universe can be either stable or saddle depending on the parameters of the theory. For some ranges of the parameters, this scaling fixed point and field-dominated fixed point can be simultaneously stable. Cosmic evolution will reach either the scaling attractor or the field-dominated attractor depending on the sign of the time derivative of the scalar field in the theory during the matter domination. The density parameter of dark matter can be larger than unity before reaching the scaling attractor if the deviation from Einstein’s theory of gravity is too large. For this DHOST theory, stabilities of {phi }-matter-dominated epoch (phi MDE) and field-dominated solutions are similar to the coupled dark energy models in Einstein gravity even though gravity is described by different theories. In our consideration, the universe can only evolve from the phi MDE regime to the field-dominated regime. The ghost and gradient instabilities up to linear order in cosmological perturbations have been investigated. There is no gradient instability, while the ghost instability can be avoided for some range of the model parameters.

Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling

We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made nondynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity. Focusing on a class of such modified gravity theories characterized by three functions of time, we discuss how modified gravity with two tensorial degrees of freedom can be distinguished observationally or phenomenologically from general relativity. It is checked that the theory gives the same predictions as general relativity for the parametrized post-Newtonian parameter $\ensuremath{\gamma}$ and the propagation speed of gravitational waves. We also find that there is no modification to asymptotically flat black holes at rest with respect to the preferred frame. Due to a large degree of freedom to choose the time-dependent functions in the theory, the homogeneous and isotropic cosmological dynamics can be made close to or even identical to that of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model. We investigate the behavior of cosmological perturbations in the long- and short-wavelength limits and show that in both limits the effects of modified gravity appear only through the modification of the background evolution. Finally, it is remarked that in the presence of a Galileon field in the matter sector, the scalar degree of freedom is revived, ruining the essential feature of the theory.

Sound Speed Resonance of the Stochastic Gravitational-Wave Background.

We propose a novel mechanism to test time variation of the propagation speed of gravitational waves (GWs) in light of GWs astronomy. As the stochastic GWs experience the whole history of cosmic expansion, they encode potential observational evidence of such variation. We report that, one feature of a varying GWs speed is that the energy spectrum of GWs will present resonantly enhanced peaks if the GWs speed oscillates in time at high-energy scales. Such oscillatory behavior arises in a wide class of modified gravity theories. The amplitude of these peaks can be at reach by current and forthcoming GWs instruments, hence making the underlying theories falsifiable. This mechanism reveals that probing the variation of GWs speed can be a promising way to search for new physics beyond general relativity.

Parameterised post-Newtonian formalism for the effective field theory of dark energy via screened reconstructed Horndeski theories

We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretation of the complementary measurements it is important to connect them to effectively constrain the vast gravitational model space. We establish such a connection within the framework of Horndeski scalar-tensor theories restricted to a luminal propagation speed of gravitational waves. This is possible via the reconstruction of the family of linearly degenerate covariant Horndeski actions from the set of EFT functions and the subsequent derivation of the PPN parameters from the reconstructed theory. We outline the required conditions which ensure a reconstructed Horndeski model possesses a screening mechanism that enables significant modifications on cosmological scales while respecting stringent astrophysical bounds. Employing a scaling method, we then perform the general post-Newtonian expansion of the reconstructed models to derive their PPN parameters γ and β in their screened regimes.

Constraints on dark energy models from the Horndeski theory

In light of the cosmological observations, we investigate dark energy models from the Horndeski theory of gravity. In particular, we consider cosmological models with the derivative self-interaction of the scalar field and the derivative coupling between the scalar field and gravity. We choose the self-interaction term to have an exponential function of the scalar field with both positive and negative exponents. For the function that has a positive exponent, our result shows that the derivative self-interaction term plays an important role in the late-time universe. On the other hand, to reproduce the right cosmic history, the derivative coupling between the scalar field and gravity must dominate during the radiation-dominated phase. However, the importance of such a coupling in the present universe found to be negligible due to its drastic decrease over time. Moreover, the propagation speed of gravitational waves estimated for our model is within the observational bounds, and our model satisfies the observational constraints on the dark energy equation of state.

Horndeski under the quantum loupe

With recent constraints on the propagation speed of gravitational waves, the class of scalar-tensor theories has significantly been reduced. We consider one of the surviving models still relevant for cosmology and investigate its radiative stability. The model contains operators with explicit breaking of the Galileon symmetry and we study whether they harm the re-organization of the effective field theory. Within the regime of validity we establish a non-renormalization theorem and show explicitly that the quantum corrections, to one-loop, do not detune the classical Lagrangian generating suppressed counterterms. This is striking since the non-renormalization theorem is established in the presence of a genuine Galileon symmetry breaking term.

Rotating black holes in valid vector-tensor theories after GW170817

Vector-tensor theories beyond General Relativity have widely been studied in the context of ultraviolet completion of gravity, endowing a mass to the graviton and explaining dark energy phenomena. We here construct rotating black hole solutions in vector-tensor theories valid after the binary neutron star merger event GW170817 that placed very stringent bound on the propagation speed of gravitational waves away from the speed of light. Such valid vector-tensor theories are constructed by performing a generic conformal transformation to Einstein-Maxwell theory, and the new rotating black hole solutions are constructed by applying the same conformal transformation to the Kerr-Newman solution. These theories fall outside of beyond generalized Proca theories but are within an extended class of vector-tensor theories that satisfy a degenerate condition to eliminate instability modes and are thus healthy. We find that such conformal Kerr-Newman solutions preserve the location of the singularities, event horizons and ergoregion boundary from Kerr-Newman, as well as the multipole moments and the Petrov type. On the other hand, the Hamilton-Jacobi equation is no longer separable, suggesting that the Carter-like constant does not exist in this solution. The standard Newman-Janis algorithm also does not work to construct the new solutions. We also compute the epicyclic frequencies, the location of the innermost stable circular orbits, and the Schwarzschild precession and apply the latter to the recent GRAVITY measurement to place bounds on the deviations away from Kerr-Newman for Sgr A$^*$.

Gravitational Waves, CMB Polarization, and the Hubble Tension.

The discrepancy between the Hubble parameter inferred from local measurements and that from the cosmic microwave background (CMB) has motivated careful scrutiny of the assumptions that enter both analyses. Here we point out that the location of the recombination peak in the CMB B-mode power spectrum is determined by the light horizon at the surface of last scatter and thus provides an alternative early-Universe standard ruler. It can thus be used as a cross-check for the standard ruler inferred from the acoustic peaks in the CMB temperature power spectrum and to test various explanations for the Hubble tension. The measurement can potentially be carried out with a precision of ≲2% with stage-IV B-mode experiments. The measurement can also be used to measure the propagation speed of gravitational waves in the early Universe.

Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories

We show that most classes of shift-symmetric degenerate higher-order scalar-tensor (DHOST) theories which satisfy certain degeneracy conditions are not compatible with the conditions for the existence of exact black hole solutions with a linearly time-dependent scalar field whose canonical kinetic term take a constant value. Combined with constraints from the propagation speed of gravitational waves, our results imply that cubic DHOST theories are strongly disfavored and that pure quadratic theories are likely to be the most viable class of DHOST theories. We find exact static and spherically symmetric (Schwarzschild and Schwarzschild-(anti-)de Sitter) black hole solutions in all shift-symmetric higher-derivative scalar-tensor theories which contain up to cubic order terms of the second-order derivatives of the scalar field, especially the full class of Horndeski and Gleyzes-Langlois-Piazza-Vernizzi theories. After deriving the conditions for the coupling functions in the DHOST Lagrangian that allow the exact solutions, we clarify their compatibility with the degeneracy conditions.

Probing observational bounds on scalar-tensor theories from standard sirens

Standard sirens are the gravitational wave (GW) analog of the astronomical standard candles, and can provide powerful information about the dynamics of the Universe. In this work, we simulate a catalog with 1000 standard siren events from binary neutron star mergers, within the sensitivity predicted for the third generation of the ground GW detector called Einstein telescope. After correctly modifying the propagation of GWs as input to generate the catalog, we apply our mock data set on scalar-tensor theories where the speed of GW propagation is equal to the speed of light. As a first application, we find new observational bounds on the running of the Planck mass, when considering appropriate values within the stability condition of the theory, and we discuss some consequences on the amplitude of the running of the Planck mass. In the second part, we combine our simulated standard sirens catalog with other geometric cosmological tests (Supernovae Ia and cosmic chronometers measurements) to constrain the Hu-Sawicki $f(R)$ gravity model. We thus find new and non-null deviations from the standard $\Lambda$CDM model, showing that in the future the $f(R)$ gravity can be tested up to 95\% confidence level. The results obtained here show that the statistical accuracy achievable by future ground based GW observations, mainly with the ET detector (and planed detectors with a similar sensitivity), can provide strong observational bounds on modified gravity theories.

Screening and degenerate kinetic self-acceleration from the nonlinear freedom of reconstructed Horndeski theories

We have previously presented a reconstruction of Horndeski scalar-tensor theories from linear cosmological observables. It includes free nonlinear terms which can be added onto the reconstructed covariant theory without affecting the background and linear dynamics. After discussing the uniqueness of these correction terms, we apply this nonlinear freedom to a range of different applications. First we demonstrate how the correction terms can be configured to endow the reconstructed models with screening mechanisms such as the chameleon, k-mouflage and Vainshtein effects. A further implication is the existence of classes of Horndeski models that are degenerate with standard cosmology to an arbitrary level in the cosmological perturbations. Particularly interesting examples are kinetically self-accelerating models that mimic the dynamics of the cosmological constant to an arbitrary degree in perturbations. Finally, we develop the reconstruction method further to the level of higher-order effective field theory, which under the restriction to a luminal propagation speed of gravitational waves introduces two new free functions per order. These functions determine the corresponding correction terms in the linearly reconstructed action at the same order. Our results enable the connection of linear cosmological constraints on generalised modifications of gravity and dark energy with the nonlinear regime and astrophysical probes for a more global interpretation of the wealth of forthcoming cosmological survey data.

The Effective Field Theory of Dark Energy Diagnostic of Linear Horndeski Theories After GW170817 and GRB170817A

We summarize the effective field theory of dark energy construction to explore observable predictions of linear Horndeski theories. We review the diagnostic of these theories on the correlation of the large-scale structure phenomenological functions: the effective Newton constant, the light deflection parameter, and the growth function of matter perturbations. We take this opportunity to discuss the evolution of the bounds the propagation speed of gravitational waves has undergone and use the most restrictive one to update the diagnostic.

Parity-violating gravity and GW170817

We consider gravitational waves (GWs) in generic parity-violating gravity including recently proposed ghost-free theories with parity violation as well as Chern-Simons (CS) modified gravity, and study the implications of observational constraints from GW170817/GRB 170817A. Whereas GWs propagate at the speed of light, c, in CS gravity, we point out that this is specific to CS gravity and the GW propagation speed deviates from c, in general, in parity-violating gravity. Therefore, contrary to the previous literature in which only CS gravity is studied as a concrete example, we show that GW170817/GRB 170817A can, in fact, be used to limit gravitational parity violation. Our argument implies that the constraint on the propagation speed of GWs can pin down the parity-violating sector, if any, to CS gravity.

Stealth Schwarzschild solution in shift symmetry breaking theories

We find stealth Schwarzschild solutions with a nontrivial profile of the scalar field regular on the horizon in the Einstein gravity coupled to the scalar field with the k-essence and/or generalized cubic galileon terms, which is a subclass of the Horndeski theory breaking the shift symmetry, where the propagation speed of gravitational waves coincides with the speed of light. After deriving sufficient conditions for the shift symmetry breaking theory to allow a general Ricci-flat metric solution with a nontrivial scalar field profile, we focus on the stealth Schwarzschild solution with the scalar field with or without time dependence. For the profile $\phi=\phi_0(r)$, we explicitly obtain two types of stealth Schwarzschild solutions, one of which is regular on the event horizon. The linear perturbation analysis clarifies that the kinetic term of the scalar mode identically vanishes, indicating that the scalar mode is strongly coupled. The absence of the kinetic term of the scalar mode in the quadratic action would inevitably arise for the stealth Schwarzschild solutions in the theory with a general scalar field profile depending only on the spatial coordinates. On the other hand, for the time-dependent scalar field profile, we clarify that there does not exist a stealth Schwarzschild solution in the shift symmetry breaking theories.

Non-trivial gravitational waves and structure formation phenomenology from dark energy

The detection of the GW170817/GRB170817A event improved the constraints on the propagation speed of gravitational waves, thus placing possible variations caused by dark energy under restraint. For models based on scalar fields belonging to the family of Horndeski Lagrangians, non-minimal derivative couplings are now severely constrained, entailing a substantially limited phenomenology. In this work we want to stress that there is still a plethora of dark energy models that get around this obstacle while still providing interesting phenomenologies able to distinguish them from the standard cosmology. We focus on a class involving vector fields as a proxy, but our discussion is extensible to a broader class of models. In particular, we show the possibility of having a non-minimal derivative coupling giving a non-trivial effect on scalar modes without affecting gravitational waves and the possibility of having a second tensor mode that can oscillate into gravitational waves. We also present a novel class of configurations breaking rotational invariance but with an energy-momentum tensor that is isotropic on-shell. This peculiar feature makes the scalar and vector sectors of the perturbations mix so that, even in a perfectly isotropic background cosmology, preferred direction effects can appear in the perturbations. We also comment on models that give rise to isotropic solutions when averaging over rapid oscillations of the vector fields. The explored models are classified according to distinctive field configurations that provide inequivalent realisations of the Cosmological Principle.

Gravitational waves in cold dark matter

We study the effects of cold dark matter on the propagation of gravitational waves of astrophysical and primordial origin. We show that the dominant effect of cold dark matter on gravitational waves from astrophysical sources is a small frequency dependent modification of the propagation speed of gravitational waves. However, the magnitude of the effect is too small to be detected in the near future. We furthermore show that the spectrum of primordial gravitational waves in principle contains detailed information about the properties of dark matter. However, depending on the wavelength, the effects are either suppressed because the dark matter is highly non-relativistic or because it contributes a small fraction of the energy density of the universe. As a consequence, the effects of cold dark matter on primordial gravitational waves in practice also appear too small to be detectable.

Using gravitational wave to test general relativity

The first direct detection of gravitational wave was realized by LIGO on September 14, 2015. Since then gravitational wave detection progresses very rapidly. So far, LIGO has confirmed 5 gravitational wave events of binary black hole merger, including GW150914, GW151226, GW170608, GW170104 and GW170814. And one gravitational wave event of binary neutron star merger has also been detected very recently, GW170817. Besides these 6 gravitational events LIGO has one more suspected gravitational wave event of binary black hole merger LVT151012. Inspired by the gravitational wave detection, gravitational wave physics and gravitational wave astronomy develop also very rapidly since 2016. The direct detection of gravitational wave qualitatively supports the general theory of relativity. But gravitational wave detection, as experiments involving strong gravitational field and strongly dynamical space-time region, can also quantitatively tests general relativity, and even find the applicable scope of general relativity, and point out the development of gravity theory beyond general relativity. In this paper, we will introduce how to use gravitational wave to test general relativity. We will try to give a comprehensive introduction to the possible ways applying gravitational wave detection to test general relativity, including the qualitative properties of gravitational waves, the degree of freedom of gravitational waves, the speed of gravitational wave propagation and the waveform characteristics of gravitational waves.