We provide a field-theoretic algorithm of obtaining energy momentum tensor (EMT) for gravitationally coupled theories. The method is based on an auxiliary field theory and equally applicable to both minimal and non-minimal coupling. The algorithm illuminates the connection between the EMT, obtained by functional variation of the metric, and local balance of energy and momentum. Our method is of cardinal value for the proper identification of the EMT in context of non-minimally coupled gravity theories.
In this paper, we use the exact renormalisation in the context of tensor models and tensorial group field theories. As a byproduct, we rederive Gaussian universality for random tensors and provide a general power counting for Abelian tensorial field theories with a closure constraint, leading us to a only five renormalizable theories.
We reconsider the issue of whether scalar-tensor theories can admit stable wormhole configurations supported by a non-trivial radial profile for the scalar field. Using a recently proposed effective theory for perturbations around static, spherically symmetric backgrounds, we show that scalar-tensor theories of "beyond Horndeski" type can have wormhole solutions that are free of ghost and gradient instabilities. Such solutions are instead forbidden within the more restrictive "Horndeski" class of theories.
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parameterized by a scalar and a symmetric two-tensor, it is argued that, in general situat…
We compute the boundary terms and junction conditions for Horndeski's panoptic class of scalar-tensor theories, and write the bulk and boundary equations of motion in explicitly second order form. We consider a number of special subclasses, including galileon theories, and present the corresponding formulae. Our analysis opens up of the possibility of studying tunnelling between vacua in generalized scalar-tensor theories, and braneworld dynamics. The latter follows because our results are independent of spacetime dimension.
The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter $ω$. The Hamiltonian structure in both sectors are similar to the corresponding structure of 4-dimensional cases. It turns out that there is a symplectic reduction from the canonical structure of $so(D+1)$ Yang-Mills theories coupled to the scalar field to the canonical structure of the geome…
We study a modification of the Plebanski action, which generically corresponds to a bi-metric theory of gravity, and identify a subclass which is equivalent to the Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories. In this manner, scalar-tensor theories are displayed as constrained BF theories. We find that in this subclass, there is no need to impose reality of the Urbantke metrics, as also the theory with real bivectors is a scalar-tensor theory with a real Lorentzian metric. Furthermore, while under the former reality conditions instabilities can arise from a wrong sign of the scal…
We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this "shadowy" mode at both the linear and the nonlinear levels.
In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent evolution of the linearised field equations of quasi-Newtonian universes are presented. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.
We perform a Hamiltonian analysis and prove that a large class of scalar-tensor theories whose Lagrangian is given by a generic function $F\left(K_{ab},N,R_{ab},h^{ab},\nabla_a,t\right)$ is free from the Ostrogradsky ghost, and thus these theories contain at most 3 degrees of freedom at classical level.
We prove that vector fields described by the generalized Proca class of theories do not admit a consistent coupling to a gravitational sector defined by a scalar-tensor theory of the degenerate type. Under the assumption that there exists a frame in which the Proca field interacts with gravity only through the metric tensor, our analysis shows that at least one of the constraints associated with the degeneracy of the scalar-tensor sector is inevitably lost whenever the vector theory includes a coupling to the Christoffel connection.
We investigate whether the classical equivalence of $f(R)$ gravity and its formulation as scalar-tensor theory still holds at the quantum level. We explicitly compare the corresponding one-loop divergences and find that the equivalence is broken by off-shell quantum corrections, but recovered on-shell.
Scalar-tensor theories (STTs) are a widely studied alternative to General Relativity (GR) in which gravity is endowed with an additional scalar degree of freedom. Although severely constrained by solar system and pulsar timing experiments, there remains a large set of STTs which are consistent with all present day observations. In this paper, we investigate the possibility of probing a yet unconstrained region of the parameter space of STTs based on the fact that stability properties of highly compact neutron stars in these theories may radically differ from those in GR.
Scattering angle at 3PM in scalar-tensor theories using the PM-EFT formalism
Laboratoire d’étude de l’Univers et des phénomènes eXtrêmes (LUX), Observatoire de Paris, Université PSL, Sorbonne Université, CNRS（极端宇宙与现象研究实验室，巴黎天文台，巴黎文理研究大学，索邦大学）；LPENS, Département de physique, Ecole normale supérieure, Université PSL, Sorbonne Université, Université Paris Cité, CNRS（物理与环境理论物理研究所，巴黎高等师范学院，巴黎文理研究大学，索邦大学，巴黎西岱大学）；Observatoire de Paris, Université PSL, Sorbonne Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学）
It is argued that the ambiguity introduced by the renormalization in the effective action of a four-dimensional renormalizable quantum field theory is at most a local polynomial action of canonical dimension four. The allowed ambiguity in the expected stress-energy tensor of a massive scalar field is severely restricted by this fact.
We derive a variety of exact black hole solutions in a subclass of Horndeski's scalar-tensor theory possessing shift symmetry, $ϕ\toϕ+c$, and reflection symmetry, $ϕ\to-ϕ$. The theory admits two arbitrary functions of $X:=-(\partialϕ)^2/2$, and our solutions are constructed without specifying the concrete form of the two functions, implying that black hole solutions in specific scalar-tensor theories found in the literature can be extended to a more general class of theories with shift symmetry. Our solutions include a black hole in the presence of an effective cosmological constant, the Naria…
In $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar $ϕ\to ϕ+c$, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.
The evolution equations for tensor perturbations in a generic scalar tensor theory of gravity are presented. Exact solution are given for a specific class of theories and Friedmann-Lemaître-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of tensor models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.
We study the perturbative behaviour of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet term. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations in the extended scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a phase transition of the topological black hole to a hairy configuration.
We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with A_5 = 0, namely when the canonical momenta conjugate to the spatial metric are linear in the extrinsic curvature, we prove that the number of physical degrees of freedom is three at fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends Horndeski's scalar-tensor gravity theory, it is protected against additional degrees of freedom.
We consider Higher-Order Scalar-Tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that are either DHOST or U-degenerate and that are quadratic in second derivatives of the scalar field, and discuss its extension to cubic and higher order theories. Working with a simple example of U-degenerate theory, we find that, for configurations in which the scalar field gradient is time-like, the apparent extra mode in such a theory can be understood as a…
We discuss the two-particle irreducible (2PI) effective action for the SYK model and for tensor field theories. For the SYK model the 2PI effective action reproduces the bilocal reformulation of the model without using replicas. In general tensor field theories the 2PI formalism is the only way to obtain a bilocal reformulation of the theory, and as such is a precious instrument for the identification of soft modes and for possible holographic interpretations. We compute the 2PI action for several models, and push it up to fourth order in the $1/N$ expansion for the model proposed by Witten in…
We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies.
We investigate a systematic formulation of vector-tensor theories based on the effective field theory (EFT) approach. The input of our EFT is that the spacetime symmetry is spontaneously broken by the existence of a preferred timelike direction in accordance with the cosmological principle. After clarifying the difference of the symmetry breaking pattern from the conventional EFT of inflation/dark energy, we find an EFT description of vector-tensor theories around the cosmological background. This approach not only serves as a unified description of vector-tensor theories but also highlights u…
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivativ…
This contribution reviews scalar-tensor theories whose Lagrangian contains second-order derivatives of a scalar field but nevertheless propagate only one scalar mode (in addition to the usual two tensor modes), and are thus not plagued with the Ostrodradsky instability. These theories, which encompass the so-called Horndeski and Beyond Horndeski theories, have recently been fully classified up to cubic order in second-order derivatives. After introducing these theories, I present a few phenomenological aspects. In cosmology, these theories can be included in the unified effective description o…
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.
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in any dimension and therefore form an interesting class of models for studying quantum gravity. We review the class of perturbatively renormalizable tensor field theories and some of their features.
Critical collapse in tensor-multi-scalar gravity theories is studied, and found that for any given target space all the theories conformally related belong to the same universal class. When only one scalar field is present, the universality is extended to include a class of non-linear gravity theories.
$ω(ϕ) \to \infty$ limit of scalar tensor theories are studied for traceless matter source. It is shown that the limit $ω(ϕ) \to \infty$ does not reduce a scalar tensor theory to general relativity. An exact radiation solution of scalar tensor cosmology under Nordtvedt conditions is obtained for flat Friedmann universe.
In the bibliography a certain confusion arises in what regards to the classification of the gravitational theories into scalar-tensor theories and general relativity with a scalar field either minimally or non-minimally coupled to matter. Higher-derivatives Horndeski and beyond Horndeski theories that at first sight do not look like scalar-tensor theories only add to the confusion. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar-tensor theory may be formulated, makes even harder to achieve a correct classificati…
We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and dis…
The recent simultaneous detection of gravitational waves and a gamma ray burst from a neutron star merger significantly shrank the space of viable scalar-tensor theories by demanding that the speed of gravity is equal to that of light. The survived theories belong to the class of degenerate higher order scalar-tensor theories. We study whether these theories are suitable as dark energy candidates. We find scaling solutions in the matter dominated universe that lead to de Sitter solutions at late times without the cosmological constant, realising self-acceleration. We evaluate quasi-static pert…
We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disf…
We generalize the known equivalence between higher order gravity theories and scalar tensor theories to a new class of theories. Specifically, in the context of a first order or Palatini variational principle where the metric and connection are treated as independent variables, we consider theories for which the Lagrangian density is a function f of (i) the Ricci scalar computed from the metric, and (ii) a second Ricci scalar computed from the connection. We show that such theories can be written as tensor-multi-scalar theories with two scalar fields with the following features: (i) the two di…
Recently published experimental results indicate the appeareance of unusual forces on asymmetric, electromagnetic resonant cavities. It is argued here that a particular class of scalar-tensor theories of gravity could account for this effect.
In gravity theories that exhibit spontaneous scalarization, astrophysical objects are identical to their general relativistic counterpart until they reach a certain threshold in compactness or curvature. Beyond this threshold, they acquire a non-trivial scalar configuration, which also affects their structure. The onset of scalarization is controlled only by terms that contribute to linear perturbation around solutions of general relativity. The complete set of these terms has been identified for generalized scalar-tensor theories. Stepping on this result, we study the onset on scalarization i…
We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar-tensor representation. It turns out that the stellar structure equations can be written with respect to the scalar-tensor invariants, allowing to interpret their physical role.
A specific choice of gauge is shown to imply a decoupling between the tensor and scalar components of Gravitational Radiation in the context of Brans-Dicke type theories of gravitation. The comparison of the predictions of these theories with those of General Relativity is thereby made straightforward.
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…
In this paper we consider the implications that the effect gravitational memory would have on primordial black holes, within the theoretical context of $F(R)$ related scalar-tensor theories. As we will demonstrate, under the assumption that the initial mass of the primordial black hole is such so that it evaporates today, this can potentially constrain the $F(R)$ related theories of gravity. We study two scalar-tensor models and discuss the evolution of primordial black holes created at some initial time $t_f$ in the early universe. The results between the two models vary significantly which s…
We discuss the relation between canonical and metric energy-momentum tensors for field theories with actions that can depend on the higher derivatives of tensor fields in a flat spacetime. In order to obtain it we use a modification of the Noether's procedure for curved space-time. For considered case the difference between these two tensors turns out to have more general form than for theories with no more than first order derivatives. Despite this fact we prove that the difference between corresponding integrals of motion still has the form of integral over 2-dimensional surface that is infi…
The problem of determining the post-Newtonian parameter $γ$ in massive scalar-tensor theories is considered. We demonstrate equivalent correspondence between the post-Newtonian parameter $γ$ and the parameter appearing in the equation of null geodysic in massive scalar-tensor theories. We show that massive scalar-tensor theories can be distinguished from general relativity based on the predictions of Shapiro time delay. All calculations are presented using hybrid metric-Palatini f(R)-gravity as an example. The expression for Shapiro time delay in hybrid f(R)-gravity is obtained for the first t…
We have shown that, within the context of Scalar-Tensor theories, the anisotropic Bianchi-type cosmological models evolve towards de Sitter universe. A similar result holds in the case of cosmology in Lyra manifold. Thus the analogue of cosmic no-hair theorem of Wald (1983) hold in both the cases. In fact, during inflation there is no difference between scalar-tensor theories, Lyra's manifold and general relativity (GR).
Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized…
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
Sub-horizon perturbations in scalar-tensor theories have been shown to grow generically faster than in uncoupled models due to a positive, additive Yukawa force. In such cases, the amount of clustering becomes larger than in the standard cosmological model, exacerbating the observed tension in the $σ_8$ parameter. Here we show instead that in some simple cases of conformally coupled dark energy one can obtain a transient regime of negative Yukawa force, without introducing ghosts or other instabilities.
Kinetic mixing between the metric and scalar degrees of freedom is an essential ingredient in contemporary scalar-tensor theories. This often makes hard to understand their physical content, especially when derivative mixing is present, as it is the case for Horndeski action. In this work we develop a method that allows to write a Ricci curvature-free scalar field equation and discuss some of the advantages of such rephrasing in the study of stability issues in the presence of matter, the existence of an Einstein frame and the generalization of the disformal screening mechanism. For quartic Ho…
We construct models of slowly rotating, perfect-fluid neutron stars by extending the classical Hartle-Thorne formalism to generic scalar-tensor theories of gravity. Working at second order in the dimensionless angular momentum, we compute the mass M, radius R, scalar charge q, moment of inertia I and spin-induced quadrupole moment Q, as well as the tidal and rotational Love numbers. Our formalism applies to generic scalar-tensor theories, but we focus in particular on theories that allow for spontaneous scalarization. It was recently discovered that the moment of inertia, quadrupole moment and…
We construct the consistent ghost-free covariant scalar-vector-tensor gravity theories with second order equations of motion with derivative interactions. We impose locality, unitarity, Lorentz invariance and pseudo-Riemannian geometry as the fundamental terms. In the tensor sector we require diffeomorphism invariance, whereas we allow the vector sector to be gauge invariant or not. The resulting Lagrangians consist of new genuine couplings among these fields with at most two derivatives per field. They propagate five physical degrees of freedom in the gauge invariant case and six degrees of f…
This article reviews scalar-tensor theories characterized by a Lagrangian that, despite the presence of second order derivatives, contain a single scalar degree of freedom. These theories, known as Degenerate Higher-Order Scalar-Tensor (DHOST) theories, include Horndeski and Beyond Horndeski theories. They propagate a single scalar mode as a consequence of the degeneracy of their Lagrangian and, therefore, are not plagued by an Ostrodradsky instability. They have been fully classified up to cubic order in second-order derivatives. The study of their phenomenological consequences restricts the …
The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models.We present general solutions corresponding to cosmological term: (i)λ(ϕ)=0$ and $(ii) λ(ϕ)=qϕ$.
The timing of binary pulsars allows us to place some of the tightest constraints on modified theories of gravity. Perhaps some of the most interesting and well-motivated extensions to General Relativity are scalar-tensor theories, in which gravity is mediated by the metric tensor and a scalar field. These theories predict large deviations from General Relativity in the presence of neutron stars through a phenomenon known as scalarization. Neutron stars in scalar-tensor theories develop scalar charges, which directly enter the timing model for binary pulsars. In this paper, we calculate and tab…
We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the tensor perturbations equations (including anisotropic stresses) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous a…
A first-order action for scalar-tensor theories of gravity is proposed. The Hamiltonian analysis of the action gives the desired connection dynamical formalism, which was derived from the geometrical dynamics by canonical transformations. It is shown that this connection formalism in Jordan frame is equivalent to the alternative connection formalism in Einstein frame. Therefore, the action principle underlying loop quantum scalar-tensor theories is recovered.
We consider the evolution of cosmological gravitational waves in scalar-tensor theory and $F(R)$ gravity theory as typical models of the modified gravity. Although the propagation speed is not changed from the speed of light, the propagation phase changes when we compare the propagation in these modified gravity theories with the propagation in the $Λ$CDM model. The phase change might be detected in future observations.
We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that in the ADM formalism Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.
