We study how the Vainshtein mechanism operates in the most general scalar-tensor theories with second-order equations of motion. The field equations of motion, which can be also applicable to most of other screening scenarios proposed in literature, are generally derived in a spherically symmetric space-time with a matter source. In the presence of a field coupling to the Ricci scalar, we clarify conditions under which the Vainshtein mechanism is at work in a weak gravitational background. We also obtain the solutions of the field equation inside a spherically symmetric body and show how they can be connected to exterior solutions that accommodate the Vainshtein mechanism. We apply our general results to a number of concrete models such as the covariant/extended Galileons and the DBI Galileons with Gauss-Bonnet and other terms. In these models the fifth force can be suppressed to be compatible with solar-system constraints, provided that non-linear field kinetic terms coupled to the Einstein tensor do not dominate over other non-linear field self-interactions.
We study the Vainshtein screening mechanism in Horndeski theories in the presence of a scalar field $ϕ$ nonminimally and kinetically coupled to ordinary matter field. A general interacting Lagrangian describing this coupling is characterized by energy transfer $f_1$ and momentum exchange $f_2$. For a spherically symmetric configurations on top of the cosmological background, we investigate the static perturbations in linear and nonlinear regimes with respect to the scalar field perturbation. In the former regime, the parametrized post-Newtonian parameter generally deviates from unity as long a…
The Horndeski theory of gravity is known as the most general scalar-tensor theory with second-order field equations. Recently, it was demonstrated by Gleyzes et al. that the Horndeski theory can further be generalized in such a way that although field equations are of third order, the number of propagating degrees of freedom remains the same. We study small-scale gravity in the generalized Horndeski theory, focusing in particular on an impact of the new derivative interaction beyond Horndeski on the Vainshtein screening mechanism. In the absence of the quintic galileon term and its generalizat…
In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor cosmological models without higher than second order derivatives in the field equation that have a fixed spatially flat de Sitter critical point for any kind of material content or vacuum energy. These models allow us to understand the current accelerated expansion of the universe as the result of the evolution towards the critical point when it is an attrac…
We propose a dark energy model where a scalar field $ϕ$ has nonlinear self-interactions in the presence of a dilatonic coupling with the Ricci scalar. This belongs to a sub-class of theories beyond Horndeski, which accommodates covariant Galileons and Brans-Dicke theories as specific cases. We derive conditions under which the scalar sound speed squared $c_{\rm s}^2$ is positive from the radiation era to today. Since $c_{\rm s}^2$ remains to be smaller than the order of 1, the deviation from Horndeski theories does not cause heavy oscillations of gauge-invariant gravitational potentials. In th…
We test the subclasses of Horndeski gravity without Vainshtein mechanism in the strong field regime of binary pulsars. We find the rate of energy losses via the gravitational radiation predicted by such theories and compare our results with observational data from quasi-circular binaries PSR J1738+0333, PSR J0737-3039, PSR J1012+5307. In addition, we consider few specific cases: the hybrid metric-Palatini f(R)-gravity and massive Brans-Dicke theory.
We describe a symmetron model in which the screening of fifth forces arises at the one-loop level through the Coleman-Weinberg mechanism of spontaneous symmetry breaking. We show that such a theory can avoid current constraints on the existence of fifth forces but still has the potential to give rise to observable deviations from general relativity, which could be seen in cold atom experiments.
Many non-linear scalar field theories possess a screening mechanism that can suppress any associated fifth force in dense environments. As a result, these theories can evade local experimental tests of new forces. Chameleon-like screening, which occurs because of non-linearities in the scalar potential or the coupling to matter, is well understood around extended objects. However, many experimental tests of these theories involve objects with spatial extent much smaller than the scalar field's Compton wavelength, and which could therefore be considered point-like. In this work, we determine ho…
New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of non-linear scalar field theories allow for a dynamical mechanism, such as the Vainshtein and chameleon ones, that suppresses the strength of the scalar fifth force in experimental environments. This is known as screening, however it is unclear how common screening is within non-linear scalar field theories. k-essence models are commonly studied examples of non…
We have previously presented a reconstruction of Horndeski scalar-tensor theories from linear cosmological observables. It includes free nonlinear terms which can be added onto the reconstructed covariant theory without affecting the background and linear dynamics. After discussing the uniqueness of these correction terms, we apply this nonlinear freedom to a range of different applications. First we demonstrate how the correction terms can be configured to endow the reconstructed models with screening mechanisms such as the chameleon, k-mouflage and Vainshtein effects. A further implication i…
We present a systematic analysis of homogeneous and isotropic cosmologies in a particular Horndeski model with Galileon shift symmetry, containing also a $Λ$-term and a matter. The model, sometimes called Fab Five, admits a rich spectrum of solutions. Some of them describe the standard late time cosmological dynamic dominated by the $Λ$-term and matter, while at the early times the universe expands with a constant Hubble rate determined by the value of the scalar kinetic coupling. For other solutions the $Λ$-term and matter are screened at all times but there are nevertheless the early and lat…
Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories propagating a single scalar degree of freedom. We first develop an effective approach to parameterize cosmological perturbations beyond linear order for these theories. In the quasi-static limit, the fully nonlinear effective Lagrangian contains six independent terms, one of which starts at cubic order in perturbations. We compute the two gravitational poten…
We consider anisotropic cosmologies in a particular shift-symmetric Horndeski theory containing the $G^{μν}\partial_μϕ\partial_νϕ$ coupling, where $G^{μν}$ is the Einstein tensor. This theory admits stable in the future self-accelerating cosmologies whose tensor perturbations propagate with the velocity very close to the speed of light such that the theory agrees with the gravity wave observations. Surprisingly, we find that the anisotropies within the Bianchi I homogeneous spacetime model are screened at early time by the scalar charge, whereas at late times they are damped in the usual way. …
Starting from the general Horndeski action, we derive the most general effective theory for scalar perturbations around flat space that allows us to screen fifth forces via the Vainshtein mechanism. The effective theory is described by a generalization of the Galileon Lagrangian, which we use to study the stability of spherically symmetric configurations exhibiting the Vainshtein effect. In particular, we discuss the phenomenological consequences of a scalar-tensor coupling that is absent in the standard Galileon Lagrangian. This coupling controls the superluminality and stability of fluctuati…
The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or…
Light bosonic fields mediate long range forces between objects. If these fields have self-interactions, i.e., non-quadratic terms in the potential, the experimental constraints on such forces can be drastically altered due to a screening (chameleon) or enhancement effect. We explore how technically natural values for such self-interaction coupling constants modify the existing constraints. We point out that assuming the existence of these natural interactions leads to new constraints, contrary to the usual expectation that screening leads to gaps in coverage. We discuss how screening can turn …
We bring together two popular formalisms which generically parameterise deviations from General Relativity on astrophysical and cosmological scales, namely the parameterised post-Newtonian (PPN) formalism and the effective field theory (EFT) of dark energy and modified gravity. These separate formalisms are successfully applied to independently perform tests of gravity in their respective regimes of applicability on vastly different length scales. Nonlinear screening mechanisms indeed make it imperative to probe General Relativity across a wide range of scales. For a comprehensive interpretati…
We consider Horndeski cosmological models able to screen the vacuum energy coming from any field theory assuming that after this screening the space should be in a de Sitter vacuum with a particular value of the cosmological constant specified by the theory of gravity itself. The most general scalar-tensor cosmological models without higher than second order derivatives in the field equations that have a spatially flat de Sitter critical point for any kind of material content or vacuum energy are, therefore, presented. These models could allow us to understand the current accelerated expansion…
Cross-correlating two different types of galaxy gives rise to parity breaking in the correlation function that derives from differences in the galaxies' properties and environments. This is typically associated with a difference in galaxy bias, describing the relation between galaxy number density and dark matter density, although observational effects such as magnification bias also play a role. In this paper we show that the presence of a screened fifth force adds additional degrees of freedom to the correlation function, describing the effective coupling of the force to the two galaxy popul…
Well-tempering stands among the few classical methods of screening vacuum energy to deliver a late-time, low energy vacuum state. We build on the class of Horndeski models that admit a Minkowski vacuum state despite the presence of an arbitrarily large vacuum energy to obtain a much larger family of models in teleparallel Horndeski theory. We set up the routine for obtaining these models and present a variety of cases, all of which are able to screen a natural particle physics scale vacuum energy using degeneracy in the field equations. We establish that well-tempering is the unique method of …
We investigate linear and non-linear dynamics of spherically symmetric perturbations on a static configuration in scalar-tensor theories focusing on the chameleon screening mechanism. We particularly address two questions: how much the perturbations can source the fifth force when the static background is well screened, and whether the resultant fifth force can change the stability and structure of the background configuration. For linear perturbations, we derive a lower bound for the square of the Fourier mode frequency $ω^2$ using the adiabatic approximation. There may be unstable modes if t…
For a massive vector field with derivative self-interactions, the breaking of the gauge invariance allows the propagation of a longitudinal mode in addition to the two transverse modes. We consider generalized Proca theories with second-order equations of motion in a curved space-time and study how the longitudinal scalar mode of the vector field gravitates on a spherically symmetric background. We show explicitly that cubic-order self-interactions lead to the suppression of the longitudinal mode through the Vainshtein mechanism. Provided that the dimensionless coupling of the interaction is n…
In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the conical singularity arises at the center of a spherically symmetric body ($r=0$) in the case where the parameter $α_{{\rm H}4}$ characterizing the deviation from the Horndeski Lagrangian $L_4$ approaches a non-zero constant as $r \to 0$. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian $L_5$ does not modify the divergent property of the Ricci scalar $R$ induced by the non-zero $α_{{\rm H}4}$. Provided that $α_{{\rm H}4}=0$, curvature scalar quantities can…
Scalar-tensor theories are frequently only consistent with fifth force constraints in the presence of a screening mechanism, namely in order to suppress an otherwise unacceptably large coupling between the scalar and ordinary matter. Here we investigate precisely which subsets of Horndeski theories do not give rise to and/or require such a screening mechanism. We investigate these subsets in detail, deriving their form and discussing how they are restricted upon imposing additional bounds from the speed of gravitational waves, solar system tests and cosmological observables. Finally, we also i…
This work studies relativistic stars in beyond Horndeski scalar-tensor theories that exhibit a breaking of the Vainshtein mechanism inside matter, focusing on a model based on the quartic beyond Horndeski Lagrangian. We self-consistently derive the scalar field profile for static spherically symmetric objects in asymptotically de Sitter space-time and show that the Vainshtein breaking branch of the solutions is the physical branch thereby resolving several ambiguities with non-relativistic frameworks. The geometry outside the star is shown to be exactly Schwarzschild-de Sitter and therefore th…
Standard sirens have been proposed as probes of alternative theories of gravity, such as Horndeski models. Hitherto, all studies have been conducted on a homogeneous-isotropic cosmological background, which is unable to consistently account for realistic distributions of matter, and for inhomogeneities in the Horndeski scalar field. Yet, the latter are essential for screening mechanisms. In this article, we comprehensively analyze the propagation of Horndeski gravitational waves in an arbitrary background spacetime and scalar field. We restrict to the class of theories in which gravitational w…
Many theories of modified gravity, including the well studied Horndeski models, are characterized by a screening mechanism that ensures that standard gravity is recovered near astrophysical bodies. In a recently introduced class of gravitational theories that goes beyond Horndeski, it has been found that new derivative interactions lead to a partial breaking of the Vainshtein screening mechanism inside any gravitational source, although not outside. We study the impact of this new type of deviation from standard gravity on the density profile of a spherically symmetric matter distribution, in …
Modifications of gravity have been considered to model the primordial inflation and the late-time cosmic acceleration. Provided that modified gravity models do not suffer from theoretical instabilities, they must be confronted with observations, not only at the cosmological scales, but also with the local tests of gravity, in the lab and in the Solar System, as well as at the astrophysical scales. Considering in particular sub-classes of the Horndeski gravity, we study their observational predictions at different scales. In order to pass the local tests of gravity while allowing for long-range…
The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher order derivatives in the equations of motion, have been identified and classified exploiting t…
Scalar field theories that possess a Vainshtein mechanism are able to dynamically suppress the associated fifth forces in the presence of massive sources through derivative non-linearities. The resulting equations of motion for the scalar are highly non-linear and therefore very few analytic solutions are known. Here we present a brief investigation of the structure of Vainshtein screening in symmetrical configurations, focusing in particular on the spherical, cylindrical and planar solutions that are relevant for observations of the cosmic web. We consider Vainshtein screening in both the Gal…
Chameleon scalar fields can screen their associated fifth forces from detection by changing their mass with the local density. These models are an archetypal example of a screening mechanism, and have become an important target for both cosmological surveys and terrestrial experiments. In particular there has been much recent interest in searching for chameleon fifth forces in the laboratory. It is known that the chameleon force is less screened around non-spherical sources, but only the field profiles around a few simple shapes are known analytically. In this work we introduce a numerical cod…
Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；International Center for Quantum-field Measurement Systems for Studies of the Universe and Particles (QUP), KEK（高能加速器研究机构（KEK）宇宙与粒子量子场测量系统国际中心）；Institute of Astrophysics, Central China Normal University（华中师范大学天体物理研究所）；Laboratory for Compact Object Astrophysics and Astronomical Technology, Central China Normal University（华中师范大学致密天体天体物理学与天文技术实验室）；Center for Theoretical Physics and College of Physics, Jilin University（吉林大学理论物理中心及物理学院）
A screening mechanism for conformal vector-tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a non-null value in low density environments. Such process occurs due to a spontaneous symmetry breaking mechanism and gives rise to both the screening of fifth forces as well as Lorentz violations. The cosmology and local constraints are also computed.
We investigate the validity of screening mechanism of the fifth force for chameleon field in highly inhomogeneous density profile. For simplicity, we consider a static and spherically symmetric system which is composed of concentric infinitely thin shells. We calculate the fifth force profile by using a numerical method for a relatively large Compton wavelength of the chameleon field. An approximate solution is also derived for the small Compton wavelength limit. Our results show that, if the thin-shell condition for the corresponding smoothed density profile is satisfied, the fifth force is s…
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…
Low-energy effective field theories containing a light scalar field are used extensively in cosmology, but often there is a tension between embedding such theories in a healthy UV completion and achieving a phenomenologically viable screening mechanism in the IR. Here, we identify the range of interaction couplings which allow for a smooth resummation of classical non-linearities (necessary for kinetic/Vainshtein-type screening), and compare this with the range allowed by unitarity, causality and locality in the underlying UV theory. The latter region is identified using positivity bounds on t…
This article investigates the properties of a scalar fifth force that arises in a scalar tensor-theory with a chameleon screening mechanism in the context of gravity space missions like the MICROSCOPE experiment. In such an experiment, the propagation of the chameleon field inside the nested cylinders of the experiment causes a fifth force when the cylinders are not perfectly co-axial. We propose a semi-analytic method to compute the field distribution and the induced fifth force and compare it to a full numerical simulation, in settings where the cylindrical symmetry is broken. The scaling of…
This paper is a pedagogical introduction to models of gravity and how to constrain them through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of General Relativity have been proposed ever since its early years. Because of Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostr…
In general, modified gravity theories are modifications or extensions of Einstein's general relativity. Some of them give rise to additional scalar degrees of freedom in Nature. If these scalar fields exist and are light enough, they should cause a gravity-like fifth force that could, in principle, exceed gravity in its strength. However, there are tight constraints on fifth forces from Solar System-based tests. Screening mechanisms are popular means for avoiding these constraints by suppressing a fifth force in regions of high environmental mass density but allowing for phenomenologically int…
We investigate the dependence of the Vainshtein screening mechanism on the cosmic web morphology of both dark matter particles and halos as determined by ORIGAMI. Unlike chameleon and symmetron screening, which come into effect in regions of high density, Vainshtein screening instead depends on the dimensionality of the system, and screened bodies can still feel external fields. ORIGAMI is well-suited to this problem because it defines morphologies according to the dimensionality of the collapsing structure and does not depend on a smoothing scale or density threshold parameter. We find that h…
In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $ϕ$ with respect to the radius $r$ vanish. If the parameter $α_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2α_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The coni…
In beyond-Horndeski theories of gravity, the Vainshtein screening mechanism might only be partially effective inside stellar objects. This results in a modification of the pressure balance equation inside stars, often characterized by a single parameter ($Υ$) in isotropic systems. We show how to constrain such theories of modified gravity, using tidal effects. We study such effects in cataclysmic variable star binaries and numerically obtain limits on the critical masses of the donor stars, below which they are tidally disrupted, by modeling them in beyond-Horndeski theories. This is contraste…
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 …
Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a "screening mechanism" is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e. a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) non-relativistic and relativistic stars. We produce screened solutions and use them as initial data for non-linear numer…
Adding a light scalar degree of freedom to General Relativity often induces a fifth force whose magnitude is strongly constrained by laboratory experiments and solar system tests. The Vainshtein screening mechanism ensures that the effects of this supplementary force are suppressed in dense environments. However, the field solution of theories exhibiting Vainshtein screening is only known in spherically symmetric situations. In this article we examine in different configurations the two-body potential energy of pointlike particles in a specific $P(X)$ theory with Vainshtein screening. We use i…
Extending general relativity by adding extra degrees of freedom is a popular approach for explaining the accelerated expansion of the Universe and to build high energy completions of the theory of gravity. The presence of such new degrees of freedom is, however, tightly constrained from several observations and experiments that aim to test general relativity in a wide range of scales. The viability of a given modified theory of gravity, therefore, strongly depends on the existence of a screening mechanism that suppresses the extra degrees of freedom. We perform simulations, and find that waves…
