Disformal theories of gravity are scalar-tensor theories where the scalar couples derivatively to matter via the Jordan frame metric. These models have recently attracted interest in the cosmological context since they admit accelerating solutions. We derive the solution for a static isolated mass in generic disformal gravity theories and transform it into the parameterised post-Newtonian form. This allows us to investigate constraints placed on such theories by local tests of gravity. The tightest constraints come from preferred-frame effects due to the motion of the Solar System with respect to the evolving cosmological background field. The constraints we obtain improve upon the previous solar system constraints by two orders of magnitude, and constrain the scale of the disformal coupling for generic models to $\mathcal{M} \gtrsim 100$ eV. These constraints render all disformal effects irrelevant for cosmology.
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…
This paper is concerned with theories of gravity that contain a scalar coupled both conformally and disformally to matter through the metric. By systematically deriving the non-relativistic limit, it is shown that no new non-linear screening mechanisms are present beyond the Vainshtein mechanism and chameleon-like screening. If one includes the cosmological expansion of the universe, disformal effects that are usually taken to be absent can be present in the solar system. When the conformal factor is absent, fifth-forces can be screened on all scales when the cosmological field is slowly-rolli…
Effective description of generalized disformal theories
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Centro de Astrofísica e Gravitação - CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术研究所天体物理学与引力中心）；Division of Liberal Arts, Kogakuin University（工学院大学人文学部）
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…
The late-time cosmological dynamics of disformal gravity are investigated using dynamical systems methods. It is shown that in the general case there are no stable attractors that screen fifth-forces locally and simultaneously describe a dark energy dominated universe. Viable scenarios have late-time properties that are independent of the disformal parameters and are identical to the equivalent conformal quintessence model. Our analysis reveals that configurations where the Jordan frame metric becomes singular are only reached in the infinite future, thus explaining the natural pathology resis…
We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This lead…
The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and properties are worth analyzing along the experience accumulated in the latter context. Here, we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for scalar-tensor theories a la Brans-Dicke.
The Jordan frame action for general disformal theories is presented and studied for the first time, motivated by several unresolved mysteries that arise when working in the Einstein frame. We present the Friedmann equations and, specialising to exponential functions, study the late-time cosmology using dynamical systems methods and by finding approximate solutions. Our analysis reveals that either the disformal effects are irrelevant or the universe evolves towards a phantom phase where the equation of state of dark energy is $-3$. There is a marginal case where the asymptotic state of the uni…
We study the impact of a modified expansion rate on the dark matter relic abundance in a class of scalar-tensor theories. The scalar-tensor theories we consider are motivated from string theory constructions, which have conformal as well as disformally coupled matter to the scalar. We investigate the effects of such a conformal coupling to the dark matter relic abundance for a wide range of initial conditions, masses and cross-sections. We find that exploiting all possible initial conditions, the annihilation cross-section required to satisfy the dark matter content can differ from the thermal…
We study the role of field redefinitions in general scalar-tensor theories. In particular, we first focus on the class of field redefinitions linear in the spin-2 field and involving derivatives of the spin-0 mode, generically known as disformal transformations. We start by defining the action of a disformal transformation in the tangent space. Then, we take advantage of the great economy of means of the language of differential forms to compute the full transformation of Horndeski's theory under general disformal transformations. We obtain that Horndeski's action maps onto itself modulo a red…
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…
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…
We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These conditions allow us to systematically construct the inverse transformation in a fully covariant manner. Applying the invertible generalized disformal transformation to known ghost-free scalar-tensor theories, we obtain a novel class of ghost-free scalar-tensor theories, whose action contains the third- or higher-order derivatives of the scalar field as well as no…
We present a general formulation to analyze the structure of slowly rotating relativistic stars in a broad class of scalar-tensor theories with disformal coupling to matter. Our approach includes theories with generalized kinetic terms, generic scalar field potentials and contains theories with conformal coupling as particular limits. In order to investigate how the disformal coupling affects the structure of relativistic stars, we propose a minimal model of a massless scalar-tensor theory and investigate in detail how the disformal coupling affects the spontaneous scalarization of slowly rota…
It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if the field is locally static and smooth, the coupling becomes invisible in the solar system: this is the disformal screening mechanism. A cosmological model is considered where the disformal coupling triggers the onset of accelerated expansion after a scaling matter era, giving a good fit to a wide range of observational data. Moreover, the interaction leaves…
By using the relativistic precession model, we have studied frequencies of quasi-periodic oscillations in the spacetime of a disformal Kerr black hole. This black hole owns an extra disformal parameter and belongs to a class of non-stealth solutions in quadratic degenerate higher-order scalar-tensor (DHOST) theories. Our result shows that only the periastron precession frequency is related to the disformal parameter, while the azimuthal frequency and the nodal precession frequency are identical with those in the usual Kerr black hole in general relativity. Combing with the observation data of …
The no-hair theorem postulates that the only externally observable properties of a black hole are its mass, its electric charge, and its angular momentum. In scalar-tensor theories of gravity, a matter distribution around a black hole can lead to the so called "spontaneous scalarisation" instability that triggers the development of scalar hair. In the Brans-Dicke type theories, this effect can be understood as a result of tachyonic effective mass of the scalar field. Here we consider the instability in the generalised class of scalar-theories that feature non-conformal, i.e. "disformal", coupl…
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…
In this note we collect, systemise and generalise the existing results for relations between general Horndeski theories and beyond Horndeski theories via disformal transformations of metric. We derive additional disformal transformation rules relating Lagrangian functions of beyond Horndeski theory and corresponding Horndeski theory and demonstrate that some of them become singular at some moments(s) once one constructs a non-singular cosmological solution in beyond Horndeski theory that is free from ghost, gradient instabilities and strong gravity regime during the entire evolution of the sys…
Solutions-generating methods based on field redefinitions, such as conformal mapping, play an important role in investigating exact solutions in modified gravity. In this work, we explore the possibility to use disformal field redefinitions to investigate new regions of the solution space of DHOST theories. The crucial ingredient is to find suitable seed solutions to generate new exact ones for DHOST theories. We first consider a seed solution of the Einstein-Scalar system describing a naked singularity. Under suitable assumptions, we derive a no-go result showing that no black hole solution c…
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…
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 show that the no-hair theorem for scalar-tensor theories with bi-metric structure can be evaded. We find that hairy black hole solutions in the presence of an electric charge admit AdS, flat or dS asymptotics with spherical, flat, or hyperbolic base manifolds. Spherically symmetric, asymptotically flat black holes and asymptotically AdS configurations with any horizon topology are compatible with a regular scalar field on and outside the event horizon. The latter presents a rich thermodynamic behavior induced by the disformal factor that enters as a coupling parameter in the theory. In the …
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…
The Horndeski action is the most general one involving a metric and a scalar field that leads to second order field equations in four dimensions. Being the natural extension of the well known Scalar-Tensor theories, its structure and properties are worth analysing along the experience accumulated in the latter context. Here we argue that disformal transformations play, for the Horndeski theory, a similar role to that of conformal transformations for Scalar-Tensor theories a l`a Brans-Dicke. We identify the most general transformation preserving second order field equations and discuss the issu…
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…
Scalar particles coupled to the Standard Model fields through a disformal coupling arise in different theories, such as massive gravity or brane-world models. We will review the main phenomenology associated with such particles. Distinctive disformal signatures could be measured at colliders and with astrophysical observations. The phenomenological relevance of the disformal coupling demands the introduction of a set of symmetries, which may ensure the stability of these new degrees of freedom. In such a case, they constitute natural dark matter candidates since they are generally massive and …
Disformal transformation provides a map relating different scalar-tensor and vector-tensor theories and gives access to a powerful solution-generating method in modified gravity. In view of the vast family of new solutions one can achieve, it is crucial to design suitable tools to guide their construction. In this work, we address this question by revisiting the Petrov classification of disformally constructed solutions in modified gravity theories. We provide close formulas which relate the principal nulls directions as well as the Weyl scalars before and after the disformal transformation. T…
We analyse the dynamical properties of disformally transformed theories of gravity. We show that disformal transformation typically introduces novel degrees of freedom, equivalent to the mimetic dark matter, which possesses a Weyl-invariant formulation. We demonstrate that this phenomenon occurs in a wider variety of disformal transformations than previously thought.
Using the disformal solution-generating method, we construct new axisymmetric solutions in Degenerate Higher Order Scalar Tensor (DHOST) theories. The method consists in first considering a "seed" known solution in DHOST theories and then performing a disformal transformation of the metric to obtain a new solution. In vacuum, the two solutions are equivalent but they become physically inequivalent when one considers coupling to matter. In that way, we "disform" the stealth Kerr black hole solution and we obtain a first analytic rotating non-stealth solution in DHOST theories, while the associa…
The extended scalar-tensor and vector-tensor theories admit black hole solutions with the nontrivial profiles of the scalar and vector fields, respectively. The disformal transformation maps a solution in a class of the scalar-tensor or vector-tensor theories to that in another class, and hence it can be a useful tool to construct a new nontrivial solution from the known one. First, we investigate how the stationary and axisymmetric solutions in the vector-tensor theories without and with the $U(1)$ gauge symmetry are disformally transformed. We start from a stationary and axisymmetric solutio…
We have studied the shadow of a disformal Kerr black hole with an extra deformation parameter, which belongs to non-stealth rotating solutions in quadratic Degenerate Higher Order Scalar Tensor (DHOST) theory. Our result show that the size of the shadow increases with the deformation parameter for the black hole with arbitrary spin parameter. However, the effect of the deformation parameter on the shadow shape depends heavily on the spin parameter of black hole and the sign of the deformation parameter. The change of the shadow shape becomes more distinct for the black hole with the more quick…
Disformal transformations have proven to be very useful to devise models of the dark sector. In the present paper we apply such transformation to a single scalar field theory as a way to drive the field into a slow roll phase. The canonical scalar field Lagrangian, when coupled to a disformal metric, turns out to have relations to bimetric dark matter theories and to describe many specific dark energy models at various limits, thus providing a surprisingly simple parametrisation of a wide variety of models including tachyon, Chaplygin gas, K-essence and dilatonic ghost condensate. We investiga…
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.
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…
Conformal and Disformal couplings between a scalar field and matter occur naturally in general scalar-tensor theories. In D-brane models of cosmology and particle physics, these couplings originate from the D-brane action describing the dynamics of its transverse (the scalar) and longitudinal (matter) fluctuations, which are thus coupled. During the post-inflationary regime and before the onset of big-bang nucleosynthesis (BBN), these couplings can modify the expansion rate felt by matter, changing the predictions for the thermal relic abundance of dark matter particles and thus the annihilati…
We study the structure of scalar-tensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector) and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure second order equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jor…
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…
Certain modified gravity theories predict the existence of an additional, non-conformally coupled scalar field. A disformal coupling of the field to the Cosmic Microwave Background (CMB) is shown to affect the evolution of the energy density in the radiation fluid and produces a modification of the distribution function of the CMB, which vanishes if photons and baryons couple in the same way to the scalar. We find the constraints on the couplings to matter and photons coming from the measurement of the CMB temperature evolution and from current upper limits on the $μ$--distortion of the CMB sp…
In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for $f(T)$ gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz br…
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…
The canonical scalar-tensor theory model which exhibits spontaneous scalarization in the strong-gravity regime of neutron stars has long been known to predict a cosmological evolution for the scalar field which generically results in severe violations of present-day Solar System constraints on deviations from general relativity. We study if this tension can be alleviated by generalizing this model to include a disformal coupling between the scalar field $φ$ and matter, where the Jordan frame metric ${\tilde g}_{μν}$ is related to the Einstein frame one $g_{μν}$ by ${\tilde g}_{μν}=A(φ)^2 (g_{μ…
In this work we consider a cosmological model in which dark energy is portrayed by a canonical scalar field which is allowed to couple to the other species by means of a disformal transformation of the metric. We revisit the current literature by assuming that the disformal function in the metric transformation can depend both on the scalar field itself and on its derivatives, encapsulating a wide variety of scalar-tensor theories. This generalisation also leads to new and richer phenomenology, explaining some of the features found in previously studied models. We present the background equati…
We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called "mimetic" dark matter theory recently introduced by Chamsedinne and Mukhanov. These conclusions hold true irrespective of whether the scalar field in the action of the assumed scalar-tensor theory of gravity is the same or different than the scalar field involved in the transformation. …
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 …
New solutions of DHOST theories can be generated by applying a disformal tranformation to a known seed solution. We examine the nature of spherically symmetric solutions of DHOST gravity obtained by disforming static spherical scalar field solutions, or stealth solutions, of general relativity. It is shown that, in these cases, black hole horizons are never created by disforming a black hole seed. New DHOST solutions are then created by disforming two lesser known scalar field solutions of general relativity: Wyman's ``other'' solution and the Husain-Martinez-Nuñez one. These new solutions dem…
