Contrary to conformal transformations, disformal transformations can change the principal null directions of a spacetime geometry. Thus, depending on the frame a gravitational wave (GW) detector minimally couples to, the properties of GWs may change under a disformal transformation. In this paper, we provide necessary and sufficient conditions which determine whether GWs change under disformal transformations or not. Our argument is coordinate-independent and can be applied to any spacetime geometry at the fully non-linear level. As an example, we show that an exact radiative solution of massless Einstein-scalar gravity which admits only shear-free parallel transported frame is mapped to a disformed geometry which does not possess any shear-free parallel transported frame. This radiative geometry and its disformed counterpart provide a concrete example of the possibility to generate tensorial GWs from a disformal transformation at the fully non-linear level. This type of non-linear effect can be completely overlooked in the usual linear perturbation theory.
We study disformal transformations of cosmological perturbations by vector fields in theories invariant under U(1) gauge transformations. Three types of vector disformal transformations are considered: (i) disformal transformations by a single timelike vector; (ii) disformal transformations by a single spacelike vector; and (iii) disformal transformations by three spacelike vectors. We show that transformations of type (i) do not change either curvature perturbation or gravitational waves; that those of type (ii) do not change curvature perturbation but change gravitational waves; and that tho…
We study disformal transformations in the context of scalar extensions to teleparallel gravity, in which the gravitational interaction is mediated by the torsion of a flat, metric compatible connection. We find a generic class of scalar-torsion actions which is invariant under disformal transformations, and which possesses different invariant subclasses. For the most simple of these subclasses we explicitly derive all terms that may appear in the action. We propose to study actions from this class as possible teleparallel analogues of healthy beyond Horndeski theories.
We consider how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of gravitationally interacting bodies. We focus on the case of two interacting objects and we obtain the effective metric driving the dynamics of the two body system when reduced to one body in the centre of mass frame. We then concentrate on the case of a light particle in the scalar and gravitational fields generated by a heavy object and find the effects of the conformal and disformal couplings on the body's trajectory such as the advance of perihelion and the Shapiro time de…
We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode. We show that the structure of the theory is preserved under the disformal transformation. We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation. Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame…
The simplest way to modify gravity is to extend the gravitational sector to include an additional scalar degree of freedom. The most general metric that can be built in such a theory includes disformal terms, so that standard model fields move on a metric which is the sum of the space time metric and a tensor constructed from first derivatives of the scalar. In such a theory gravitational waves and photons can propagate at different speeds, and these can in turn be different from the maximum speed limit for matter particles. In this work we show that disformal couplings can cause charged parti…
Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. Specifically, these theories lie beyond the quadratic/cubic DHOST class. We explore cosmological perturbations to identify a subclass where gravitational waves propagate at the speed of light and clarify the conditions for the absence of ghost/gradient instabi…
The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the confo…
The disformal transformation of metric $g_{μν} \to Ω^2 (ϕ)g_{μν}+Γ(ϕ,X) \partial_μϕ\partial_νϕ$, where $ϕ$ is a scalar field with the kinetic energy $X= \partial_μϕ\partial^μϕ/2$, preserves the Lagrangian structure of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories (which is the minimum extension of Horndeski theories). In the presence of matter, this transformation gives rise to a kinetic-type coupling between the scalar field $ϕ$ and matter. We consider the Einstein frame in which the second-order action of tensor perturbations on the isotropic cosmological background is of the same form as…
Matter coupling in modified gravity theories is a nontrivial issue when the gravitational Lagrangian possesses a degeneracy structure to avoid the problem of the Ostrogradsky ghost. Recently, this issue was addressed for bosonic matter fields in the generalized disformal Horndeski class, which is so far the most general class of ghost-free scalar-tensor theories obtained by performing a higher-derivative generalization of invertible disformal transformations on Horndeski theories. In this paper, we clarify the consistency of fermionic matter coupling in the generalized disformal Horndeski theo…
Motivated by the GW170817/GRB170817A constraint on the deviation of the speed of gravitational waves from that of photons, we study disformal transformations of the metric in the context of the generalized Proca theory. The constraint restricts the form of the gravity Lagrangian, the way the electromagnetism couples to the gravity sector on cosmological backgrounds, or in general a combination of both. Since different ways of coupling matter to gravity are typically related to each other by disformal transformations, it is important to understand how the structure of the generalized Proca Lagr…
We study the frame dependence/independence of cosmological observables under disformal transformations, extending the previous results regarding conformal transformations, and provide the correspondence between Jordan-frame and Einstein-frame variables. We consider quantities such as the gravitational constant in the Newtonian limit, redshift, luminosity and angular diameter distances, as well as the distance-duality relation. Also, the Boltzmann equation, the observed specific intensity, and the adiabaticity condition are discussed. Since the electromagnetic action changes under disformal tra…
It is shown that a disformally coupled theory in which the gravitational sector has the Einstein-Hilbert form is equivalent to a quartic DBI Galileon Lagrangian, possessing non-linear higher derivative interactions, and hence allowing for the Vainshtein effect. This Einstein Frame description considerably simplifies the dynamical equations and highlights the role of the different terms. The study of highly dense, non-relativistic environments within this description unravels the existence of a disformal screening mechanism, while the study of static vacuum configurations reveals the existence …
When augmenting our cosmological models or gravitational theories with an additional light scalar field, any coupling between matter and this scalar can affect the orbital motion of binary systems. Ordinarily, the new force mediated by the scalar can be naturally the same order of magnitude as the usual gravitational force and therefore is tightly constrained. We show that a disformal coupling between the scalar and matter can lead to a novel screening mechanism in which these fifth forces are suppressed by several orders of magnitude at sufficiently small separations and large relative veloci…
The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of…
We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories. Scalar-dependent disformal transformations have been investigated in this context, and our focus is understanding the transformations that depend on more general fields. We show that vector-dependent disformal couplings can be obtained in various different ways, each leading to spontaneous vectorization as indicated by the instabilities in linearized equations of mo…
Arnold Sommerfeld Center for Theoretical Physics（阿诺德·索末菲理论物理中心）；Univ de Lyon, ENS de Lyon, Laboratoire de Physique, CNRS UMR 5672（里昂大学，里昂高等师范学校，物理实验室，法国国家科学研究中心）；Sede Esmeralda, Universidad de Tarapacá（塔拉帕卡大学埃斯梅拉达校区）
We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under…
It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric $g_{μν} \to Ω^2(ϕ)g_{μν}+Γ(ϕ,X) \nabla_μ ϕ\nabla_ν ϕ$, where $Ω$ is a function of a scalar field $ϕ$ and $Γ$ is another function depending on both $ϕ$ and $X=g^{μν}\nabla_μ ϕ\nabla_ν ϕ$. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompa…
In this work we study the role of disformal transformation on cosmological backgrounds and its relation to the speed of sound for tensor modes. A speed different from one for tensor modes can arise in several contexts, such as Galileons theories or massive gravity, nevertheless the speed is very constrained to be one by observations of gravitational wave emission. It has been shown that in inflation a disformal trans- formation allows to set the speed for tensor modes to one without making changes to the curvature power spectrum. Here we show that this invariance does not hold when considering…
We consider a disformal coupling between Standard Model matter and a cubic Galileon scalar sector, assumed to be a relict of some other physics that solves the cosmological constant problem rather than a solution in its own right. This allows the energy density carried by the Galileon scalar to be sufficiently small that it evades stringent constraints from the integrated Sachs-Wolfe effect, which otherwise rules out the cubic Galileon theory. Although the model with disformal coupling does not exhibit screening, we show there is a `screening-like' phenomenon in which the energy density carrie…
Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order. In some cases, this is a mere consequence of a disformal field redefinition carried out in a non-degenerate theory. More generally, this is made possible by the existence of an additional constraint that removes the would-be ghost. It has been noted that this constraint can be thwarted when the coupling to matter involves time derivatives of the metric, which results in a modification of the canonical momenta of the gravitationa…
Apparent Lorentz violation from disformally coupled ultralight dark matter
Leibniz University Hannover（汉诺威莱布尼茨大学）；Max Planck Institute for Gravitational Physics, Albert Einstein Institute（马克斯·普朗克引力物理研究所，阿尔伯特·爱因斯坦研究所）；Weizmann Institute of Science（魏茨曼科学研究所）；Center for Physical Sciences and Technology（物理科学与工程技术中心）
Disformal Maps: Classification and Singular Dynamics
Institute for Basic Science (IBS)（基础科学研究所）；CEICO - Central European Institute for Cosmology and Fundamental Physics, FZU - Institute of Physics of the Czech Academy of Sciences（中欧宇宙学与基础物理中心、捷克科学院物理研究所）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Department of Physics & Institute of Physics and Applied Physics (IPAP), Yonsei University（延世大学物理系与应用物理研究所）
Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However, spin effects are still relatively unexplored in this context. In this work, we construct an effective point-particle action for a generic spinning body that can couple both conformally and disformally to a real scalar field, and we show that requiring the existence of a self-consistent solution automatically implies that if a scalar couples to the mass of a …
We disclose remarkable features of the scalar-tensor theory with the derivative coupling of the scalar field to the curvature in the Palatini formalism. Using the disformal transformations, we show that this theory is free from Otrogradski ghosts. For a special relation between two coupling constants, it is disformally dual to the Einstein gravity minimally coupled to the scalar, which opens the way to constructing several exact solutions. The disformal transformation degenerates at the boundary of the physical region, near which the properties of desingularization are revealed, illustrated by…
We re-examine the problem of parity violation in single field inflation. We look for a systematic way to parametrically approach the scale at which maximal parity violation occurs, which is where we expect to find the presence of the Chern Simons instability. We do so by considering possible realizations of the effective field theory of Scalar-Tensor gravity, which could offer a rich phenomenology. The gravitational action is extended to include derivatively coupled interactions which, by means of a disformal transformation, are scaled by negative powers of a small parameter which is identifie…
We show that if the propagating speed of gravitational waves (GWs) gradually diminishes during inflation, the power spectrum of primordial GWs will be strongly blue, while that of the primordial scalar perturbation may be unaffected. We also illustrate that such a scenario is actually a disformal dual to the superinflation, but it does not have the ghost instability. The blue tilt obtained is $0<n_T\lesssim 1$, which may significantly boost the stochastic GWs background at the frequency band of Advanced LIGO/Virgo, as well as the space-based detectors.
We explore general scalar-tensor models in the presence of a kinetic mixing between matter and the scalar field, which we call Kinetic Matter Mixing. In the frame where gravity is de-mixed from the scalar this is due to disformal couplings of matter species to the gravitational sector, with disformal coefficients that depend on the gradient of the scalar field. In the frame where matter is minimally coupled, it originates from the so-called beyond Horndeski quadratic Lagrangian. We extend the Effective Theory of Interacting Dark Energy by allowing disformal coupling coefficients to depend on t…
We investigate the gravitational waves phenomena in the geometric scalar theory of gravity (GSG) that belongs to a class of theories such that gravity is described by a single scalar field. The associated physical metric describing the spacetime is constructed from a disformal transformation of Minkowski geometry. In this theory, a weak field approximation gives rise to a description similar to that one obtained in general relativity, although the gravitational waves in GSG have a characteristic longitudinal polarization mode, besides others modes that are observer dependent. We also analyze t…
In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range of gravitational theories including Horndeski theories, its generalization, and the theories with spatial derivatives higher than second order (e.g., Horava-Lifshitz gravity). We obtain the inflationary power spectrum of tensor modes by taking into account corrections induced by higher-order spatial derivatives and slow-roll corrections to the de Sitter back…
Unique gravitational wave signatures of GLPV scalar-tensor theories
Leibniz University Hannover（汉诺威莱布尼茨大学）；Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut（马克斯·普朗克引力物理研究所，阿尔伯特·爱因斯坦研究所）；Institute for Basic Science (IBS)（基础科学研究院）；Institute of Science Tokyo（东京科学大学）；Yonsei University（延世大学）
It is investigated the gravitational waves phenomena in the geometric scalar theory of gravity (GSG), a class of theories such that gravity is described by a single scalar field. The associated physical metric describing the spacetime is constructed from a disformal transformation of Minkowski geometry. In this theory, a weak field approximation gives rise to a description similar to that one obtained in general relativity, with the gravitational waves propagating at the same speed as the light, although they have a characteristic longitudinal polarization mode, besides others modes that are o…
The Galileon model is a tensor-scalar theory of gravity which explains the late acceleration of the Universe expansion with no instabilities and recovers General Relativity in the strong field limit. Most constraints obtained so far on Galileon model parameters from cosmological data were derived for the limited subset of tracker solutions and reported tensions between the model and data. This paper presents the first exploration of the general solution of the Galileon model, which is confronted against recent cosmological data for both background observables and linear perturbations, using Mo…
Modified gravity theories with an effective Newton constant that varies over cosmological timescales generally predict a different gravitational wave luminosity distance than General Relativity. While this holds for a uniform variation, we show that if locally screened at the source and at the observer as required to pass stringent astrophysical tests of gravity, the General Relativistic distance is restored. In the absence of such a screening, the same effect must modify electromagnetic luminosity distances inferred from supernovae Type Ia, to the extent that the effects can cancel in the com…
We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity. Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions. After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories. It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational wave…
It is important to re-examine some of the interactions of gravitational waves with matter due to the recent discovery of the waves in LIGO. In a previous paper with Morales, interaction of gravitational waves was studied with scalar and neutrino fields in Minkowski space-time. In this paper, we find that electromagnetic waves have a similar interaction with gravitational wave in a flat background, and we comment on the implications of this for a gravitational wave detector. Primordial gravitational waves were generated in the early universe and thus it is important to study interaction of the …
In this paper we introduce a new approach to the study of the effects that an impulsive wave, containing a mixture of material sources and gravitational waves, has on a geodesic congruence that traverses it. We find that the effect of the wave on the congruence is a discontinuity in the B-tensor of the congruence. Our results thus provide a detector independent and covariant characterization of gravitational memory.
It is of fundamental importance to know the mass of gravitons. A simple method for constraining the graviton mass is to compare the arrival time of light and that of gravitational waves provided that both waves are simultaneously emitted from the same source. To date, from observations of gravitational waves by the LIGO, the upper bound on the graviton mass $m_g$ is given by $m_g\lesssim 5.0 \times 10^{-23}$eV. However, when we compare the arrival time of light and gravitational waves, lensing effects could be important for some cases. Moreover, in many cases, the wavelength of gravitational w…
The LIGO/VIRGO collaboration has recently announced the detection of gravitational waves from a neutron star-neutron star merger (GW170817) and the simultaneous measurement of an optical counterpart (the gamma-ray burst GRB 170817A). The close arrival time of the gravitational and electromagnetic waves limits the difference in speed of photons and gravitons to be less than about one part in $10^{15}$. This has three important implications for cosmological scalar-tensor gravity theories that are often touted as dark energy candidates and alternatives to $Λ$CDM. First, for the most general scala…
Modified Newtonian Dynamics is an empirical modification to Poisson's equation which has had success in accounting for the `gravitational field' $Φ$ in a variety of astrophysical systems. The field $Φ$ may be interpreted in terms of the weak field limit of a variety of spacetime geometries. Here we consider three of these geometries in a more comprehensive manner and look at the effect on timelike and null geodesics. In particular we consider the Aquadratic Lagrangian (AQUAL) theory, Tensor-Vector-Scalar (TeVeS) theory and Generalized Einstein-Æther (GEA) theory. We uncover a number of novel f…
We investigate how the production of gravitational waves (GWs) is affected by the GW velocity $(c_T)$ during preheating after inflation. For instance, we simulate the production of GWs after $λϕ^4$ chaotic inflation, and find that GW spectrum is enhanced for $c_T<1$, but distorted (suppressed at low frequency, but enhanced at high frequency) for $c_T>1$.
In order to detect high frequency gravitational waves, we need a new detection method. In this paper, we develop a formalism for a gravitational wave detector using magnons in a cavity. Using Fermi normal coordinates and taking the non-relativistic limit, we obtain a Hamiltonian for magnons in gravitational wave backgrounds. Given the Hamiltonian, we show how to use the magnons for detecting high frequency gravitational waves. Furthermore, as a demonstration of the magnon gravitational wave detector, we give upper limits on GHz gravitational waves by utilizing known results of magnon experimen…
We demonstrate that Huygens' principle for gravitational waves fails in quadratic gravity models that exhibit conformal symmetry at high energies. This results in the blurring of gravitational wave signals over finite timescales related to the energy scale of new physics $M_{\star}$. Furthermore, on very small scales the gravitational wave Green's function reduces to that of the wave equation in two dimensions. In principle, $M_{\star}$ could be constrained directly from gravitational wave observations.
Based on the relationship between proper distance and coordinate distance, the geometrical phenomenon caused by the passing gravitational waves can not be observed locally. The electromagnetic wave equations in the background gravitational waves are studied. We find that the expansion and contraction of wave lengths are always synchronous with the objects it measures. The background of the gravitational waves leads to dissipation and dispersion in the propagation of electromagnetic wave. The phase of the gravitational waves control the dissipation term and dispersion term in the telegrapher's …
In this short paper we investigate quantum gravitational effects on Einstein's equations using effective field theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual massless mode, we find a pair of modes with complex masses. These massive particles have a width and could thus lead to a damping of gravitational waves if excited in violent astrophysical processes producing gravitational waves such as e.g. black hole mergers. We discuss the consequences for gravitational wave events such as GW 150914 recently observed by the Adva…
We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of th…
We present an alternative derivation of the gravitational clock compass and show how such a device can be used for the detection of gravitational waves. Explicit compass setups are constructed in special types of space--times, namely for exact plane gravitational waves and for waves moving radially relative to an observer.
The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, …
