We compute the Post-Newtonian parameter (PPN),$γ$, for scalar-tensor gravity theory when the action functional for the scalar field is a non-standard one, namely the Dirac-Born-Infeld (DBI) type action, used in the literature for a tachyon field. We investigate two different cases (Linear and conformal couplings) when the scalar field is non-minimally coupled to gravity via the scalar curvature. We find that the PPN parameter $γ$, which measures the amount of space curvature per unit rest mass, becomes a function of the effective mass of the scalar field. Using this PPN parameter, we calculate the time delay $Δτ$ for the signal to travel the round trip distance bertween a ground based antenna and a reflector placed in a spacecraft which is produced due to the grvitational field of Sun. We use this $Δτ$ to compare our result with that obtained by the Cassini mission and derive the constraints on the model parameters.
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 …
We study the cosmology on the Friedmann-Lemaitre-Robertson-Walker background in scalar-vector-tensor theories with a broken $U(1)$ gauge symmetry. For parity-invariant interactions arising in scalar-vector-tensor theories with second-order equations of motion, we derive conditions for the absence of ghosts and Laplacian instabilities associated with tensor, vector, and scalar perturbations at linear order. This general result is applied to the computation of the primordial tensor power spectrum generated during inflation as well as to the speed of gravity relevant to dark energy. We also const…
The $f(R)$ gravity and scalar-tensor theory are known to be equivalent at the classical level. We study if this equivalence is valid at the quantum level. There are two descriptions of the scalar-tensor theory in the Jordan and Einstein frames. It is shown that these three formulations of the theories give the same determinant or effective action on shell, and thus they are equivalent at the quantum one-loop level on shell in arbitrary dimensions. We also compute the one-loop divergence in $f(R)$ gravity.
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…
In this work we study the cosmological attractor models of inflation in connection with certain scalar-tensor theories of gravity, e.g $f(R)$ gravity and Brans-Dicke theory. For some particular choices of the functional degrees of freedom in these theories, one obtains Starobinsky like predictions in the ($n_s$-$r$) observable plane. We have demonstrated that these choices in the Lagrangian density of certain $f(R)$ and Brans-Dicke theories fulfil the condition of the cosmological attractors. That explains why known predictions of $f(R)$ and Brans-Dicke theories in certain cases appear to be t…
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.
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 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…
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.
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…
We compare Mercury's precession test in standard General Relativity (GR), Brans-Dicke theories (BD), and Palatini f(R)-theories. We avoid post Newtonian (PN) approximation and compute exact precession in these theories. We show that the well-known mathematical equivalence between Palatini f(R)-theories and a specific subset of BD theories does not extend to a really physical equivalence among theories since equivalent models still allow different incompatible precession for Mercury depending on the solution one chooses. As a result one cannot use BD equivalence to rule out Palatini f(R)-theori…
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.
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.
Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which shows that the speed of gravitational waves, $c_g$, is the same as the speed of light, within deviations of order $10^{-15}$. This observation implies very severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of Degenerate …
The equivalence between theories depending on the derivatives of $R$, i.e. $f\left( R,\nabla R,...,\nabla^{n}R\right) $, and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that $f\left( R,\nabla R,...,\nabla^{n}R\right) $ theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms $ω_{0}=0$ and $ω_{0}= - \frac{3}{2}$ for metric and Palatini formalisms respectively. This result is analogous to what happens for $f(R)$ theories. It is worthy emphasizing that the scalar-multi-tensor…
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.
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.
Degenerate higher-order scalar-tensor (DHOST) theories are considered the most general class of scalar-tensor theories so that any constraints on them apply to the full set of scalar-tensor models. DHOST theories modify the laws of gravity even at galaxy clusters scale hence affecting the weak lensing (WL), X-ray and Sunyaev-Zel'dovich observables. We derive the theoretical expression for the lensing convergence $κ$, and the pressure profile $P$, of clusters in the framework of DHOST theories, and quantify how much they deviate from their General Relativity (GR) counterparts. We argue that com…
Equivalence of scalar-tensor theories and scale-dependent gravity
Technische Universität Wien（维也纳工业大学）；Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；Radboud University（拉德堡德大学）；Silesian University in Opava（奥帕瓦西里西亚大学）；Universitat Politècnica de València（巴伦西亚理工大学）
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）
