We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations.
Metric $f(R)$ gravity theories behave like GR with cosmological constant when $f"(R)$ = 0, and like scalar-tensor theories elsewhere. I investigate the transition from $f"(R) \neq 0$ to $f"(R) = 0$, and show that this theory may offer a way to explain Dark Energy and/or Dark Matter without having to make use of the chameleon mechanism to agree with solar system tests.
We consider the possibility of the detection of a chameleon effect by an earth orbiting satellite such as LAGEOS, and possible constraints that might be placed on chameleon model parameters. Approximate constraints presented here result from using a simple monopole approximation for the gravitational field of the earth, along with results from the Khoury-Weltman chameleon model, solar system constraints obtained from the Cassini mission, and parameter bounds obtained from the LAGEOS satellite. It is furthermore suggested that a comparison of ground-based and space-based multipole moments of th…
We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified g…
On cosmological scales, observations of the cluster abundance currently place the strongest constraints on f(R) gravity. These constraints lie in the large-field limit, where the modifications of general relativity can correctly be modeled by setting the Compton wavelength of the scalar field to its background value. These bounds are, however, at the verge of penetrating into a regime, where the modifications become nonlinearly suppressed due to the chameleon mechanism and cannot be described by this linearized approximation. For future constraints based on observations subjected to cluster ab…
We consider cosmological models where dark energy is described by a dynamical field equipped with the Chameleon screening mechanism, which serves to hide its effects in local dense regions and to conform to Solar System observations. In these models, there is no universal gravitational coupling and here we study the effective couplings that determine the force between massive objects, $G_N$, and the propagation of gravitational waves, $G_{gw}$. In particular, we revisit the Chameleon screening mechanism without neglecting the time dependence of the galactic environment where local regions are …
The Solar System bounds on R^n gravity are often ignored in the literature by invoking the chameleon mechanism. We show that in order for the latter to work, the exponent n must be ridicolously close to unity and, therefore, these theories are severely constrained.
In this work, we consider an emergent universe in generalized gravity theories like the chameleon, f(R) and f(T) gravities. We reconstruct the potential of the chameleon field under the emergent scenario of the universe and observe its increasing nature with the evolution of the universe. We reveal that in the emergent universe scenario, the equation-of-state parameter behaves like quintessence in the case of f(R) gravity and like phantom in the case of f(T) gravity.
In chameleon dark energy models, local gravity constraints tend to rule out parameters in which observable cosmological signatures can be found. We study viable chameleon potentials consistent with a number of recent observational and experimental bounds. A novel chameleon field potential, motivated by f(R) gravity, is constructed where observable cosmological signatures are present both at the background evolution and in the growth-rate of the perturbations. We study the evolution of matter density perturbations on low redshifts for this potential and show that the growth index today gamma_0 …
We study the field profile of a scalar field $ϕ$ that couples to a matter fluid (dubbed a chameleon field) in the relativistic gravitational background of a spherically symmetric spacetime. Employing a linear expansion in terms of the gravitational potential $Φ_c$ at the surface of a compact object with a constant density, we derive the thin-shell field profile both inside and outside the object, as well as the resulting effective coupling with matter, analytically. We also carry out numerical simulations for the class of inverse power-law potentials $V(ϕ)=M^{4+n} ϕ^{-n}$ by employing the info…
Chameleon fields may modify gravity on cluster scales while recovering general relativity locally. This article reviews signatures of chameleon modifications in the nonlinear cosmological structure, comparing different techniques to model them, summarising the current state of observational constraints, and concluding with an outlook on prospective constraints from future observations and applications of the analytic tools developed in the process to more general scalar-tensor theories. Particular focus is given to the Hu-Sawicki and designer models of f(R) gravity.
We investigate the solar-system constraint on the f(R) theory of modified gravity with chameleon mechanism, where f(R) represents the deviation from general relativity in the gravity action. We obtain a stringent bound to a general, non-constant deviation function f(R): -10^{-15} < df/dR < 0 when R ~ 3*10^5*H0^2, and a loose bound: 0 < R*d(df/dR)/dR < 2/5 when R > 3*10^5*H0^2, by requiring the thin-shell condition in the solar system, particularly in the atmosphere of the Earth. These bounds can be conveniently utilized to test the f(R) models with given functional forms of f(R) and to obtain …
Current constraints on f(R) gravity from the large-scale structure are at the verge of penetrating into a region where the modified forces become nonlinearly suppressed. For a consistent treatment of observables at these scales, we study cluster quantities produced in chameleon and linearized Hu-Sawicki f(R) gravity dark matter N-body simulations. We find that the standard Navarro-Frenk-White halo density profile and the radial power law for the pseudo phase-space density provide equally good fits for f(R) clusters as they do in the Newtonian scenario. We give qualitative arguments for why thi…
Chameleon $f(R)$ gravity is equivalent to a class of scalar-tensor theories of gravity with chameleon screening mechanism allowing the theory to satisfy local tests of gravity. Within the framework of chameleon $f(R)$, we study the impact of the chameleon mechanism on the orbital evolution of binary pulsars, and calculate in detail the post-Keplerian (PK) effects (periastron advance, Einstein delay, Shapiro delay, orbital period decay and eccentricity decay) of binary orbit. The differences in PK effects between general relativity (GR) and chameleon $f(R)$ are elegantly quantified by a combina…
This article investigates the profile of the scalar field of a scalar-tensor theory subject to the chameleon mechanism in the context of gravity space missions like the MICROSCOPE experiment. It analyses the experimental situations for models with an inverse power law potential that can in principle induce a fifth force inside the satellite, hence either be detected or constrained. As the mass of the scalar field depends on the local matter density, the screening of the scalar field depends crucially on both the parameters of the theory (potential and non-minimal coupling to matter) and on the…
In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have modified the N-body simulation code ECOSMOG to perform a total of 65 simulations for different models and parameter values, including the default LCDM. These simulations enable us to explore a significant portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and intere…
We consider models where moduli fields are not stabilized and play the role of quintessence. In order to evade gravitational tests, we investigate the possibility that moduli behave as chameleon fields. We find that, for realistic moduli superpotentials, the chameleon effect is not strong enough, implying that moduli quintessence models are gravitationally ruled out. More generally, we state a no-go theorem for quintessence in supergravity whereby models either behave like a pure cosmological constant or violate gravitational tests
In this work, we derive the analytical form for a $f(R)$ model that describes a perfect scalar field $ϕ$ by assuming the existence of a chameleon mechanism. Based on four statements, at the background and perturbative level, it is possible to relate the extra terms from this theory as a geometrical perfect fluid term, whose has been expressed as possible candidates to explain the nature of the dark sector, and possibly, in the case of a perfect scalar chameleon during inflation, satisfy the big bang nucleosynthesis (BBN) constraints until late times.
In conventional approach to the chameleon mechanism, by assuming a static and spherically symmetric solutions in which matter density and chameleon field are given by $ρ=ρ(r)$ and $ϕ=ϕ(r)$, it has been shown that mass of chameleon field is matter density-dependent. In regions of high matter density such as earth, chameleon field is massive, in solar system it is low and in cosmological scales it is very low. In this article we revisit the mechanism in cosmological scales by assuming a redshift dependence of the matter density and chameleon field, i.e. $ρ=ρ(z)$, $ϕ=ϕ(z)$. To support our analysi…
It is widely believed that the screening mechanism is an essential feature for the modified gravity theory. Although this mechanism has been examined thoroughly in the past decade, their analyses are based on the classical configuration of the matter fields. In this paper, we demonstrate a new formulation of the chameleon mechanism in $F(R)$ gravity theory, to shed light on quantum-field theoretical effects on the chameleon mechanism as well as the related scalaron physics, induced by the matter sector. We show a potential absence of the chameleon mechanism in the cosmic history based on a sca…
We present a novel scenario where a scalar field acquires a mass which depends on the local matter density: the field is massive on Earth, where the density is high, but is essentially free in the solar system, where the density is low. All existing tests of gravity are satisfied. We predict that near-future satellite experiments could measure an effective Newton's constant in space different than that on Earth, as well as violations of the equivalence principle stronger than currently allowed by laboratory experiments.
We consider a generalized Brans-Dicke model in which the scalar field has a potential function and is also allowed to couple non-minimally with the matter sector. This anomalous gravitational coupling can in principle avoid the model to pass local gravity experiments. One then usually assumes that the scalar field has a chameleon behavior in the sense that it acquires a density-dependent effective mass. While it can take a small effective mass in cosmological (low-density environment) scale, it has a sufficiently heavy mass in Solar System (large-density environment) and then hides gravity tes…
Light scalar fields are expected to arise in theories of high energy physics (such as string theory), and find phenomenological motivations in dark energy, dark matter, or neutrino physics. However, the coupling of light scalar fields to ordinary (or dark) matter is strongly constrained from laboratory, solar system, and astrophysical tests of fifth force. One way to evade these constraints in dense environments is through the chameleon mechanism, where the field's mass steeply increases with ambient density. Consequently, the chameleonic force is only sourced by a thin shell near the surface …
This article is dedicated to the use the MICROSCOPE mission's data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE's instrument intrinsic to its capacitive measurement system. Any discrepancy between the expected and measured stiffness may result from unaccounted-for contributors, i.e. extra-forces. This work considers the case of chameleon gravity as a possible contributor. It was previously shown that in situations similar to these measurement sessions, a chameleon fifth force appears and acts as…
We propose a version of a gravitational theory with the torsion field, induced by the chameleon field. Following Hojman et al. Phys. Rev. D17, 3141 (1976) the results, obtained in Phys. Rev. D90, 045040 (2014), are generalised by extending the Einstein gravity to the Einstein-Cartan gravity with the torsion field as a gradient of the chameleon field through a modification of local gauge invariance of minimal coupling in the Weinberg-Salam electroweak model. The contributions of the chameleon (torsion) field to the observables of electromagnetic and weak processes are calculated. Since in our a…
We analyse a non-relativistic approximation of the Dirac equation for slow fermions, coupled to the chameleon field and torsion in the spacetime with the Schwarzschild metric, taken in the weak gravitational field of the Earth approximation. We follow the analysis of the Dirac equation in the curved spacetime with torsion, proposed by Kostelecky (Phys. Rev. D69, 105009 (2004)), and apply the Foldy--Wouthuysen transformations. We derive the effective low-energy gravitational potentials for slow fermions, coupled to the gravitational field of the Earth, the chameleon field and to torsion with mi…
Theories of modified gravity where light scalars with non-trivial self-interactions and non-minimal couplings to matter-chameleon and symmetron theories-dynamically suppress deviations from general relativity in the solar system. On other scales, the environmental nature of the screening means that such scalars may be relevant. The highly-nonlinear nature of screening mechanisms means that they evade classical fifth-force searches, and there has been an intense effort towards designing new and novel tests to probe them, both in the laboratory and using astrophysical objects, and by reinterpret…
The chameleon, or generalizations thereof, is a light scalar that couple to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: i) the Compton wavelength of such a scalar can be at most Mpc at present cosmic density, which restricts its impact to non-linear scales; ii) the conformal factor relating Einstein- and Jordan…
This article extends bimetric formulations of massive gravity to make the mass of the graviton to depend on its environment. This minimal extension offers a novel way to reconcile massive gravity with local tests of general relativity without invoking the Vainshtein mechanism. On cosmological scales, it is argued that the model is stable and that it circumvents the Higuchi bound, hence relaxing the constraints on the parameter space. Moreover, with this extension the strong coupling scale is also environmentally dependent in such a way that it is kept sufficiently higher than the expansion rat…
Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f(R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then we make suitable linearizations that apply to nonrelativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleonlike mechanism can lead to a post-Newtonian parameter γ compati…
We derive the most general effective low-energy potential to order O(1/m) for slow Dirac fermions with mass m, coupled to gravitational, chameleon and torsion fields in the Einstein-Cartan gravity. The obtained results can be applied to the experimental analysis of gravitational, chameleon and torsion interactions in terrestrial laboratories. We discuss the use of rotating coordinate systems, caused by rotations of devices, for measurements of the torsion vector and tensor components, caused by minimal torsion--fermion couplings (Ivanov and Wellenzohn, Phys. Rev. D92, 065006 (2015)). Using the…
In chameleon field theories a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter, however, the chameleon mechanism also extends to the case where the coupling becomes field-dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to LCDM, but can in som…
In the chameleon mechanism, a field (typically scalar) has a mass that depends on the matter density of the environment: the larger is the matter density, the larger is the mass of the chameleon. We briefly review some aspects of chameleonic theories. In particular, in a typical class of these theories, we discuss the lagrangian, the role of conformal transformations, the equation of motion and the thin-shell effect. We also discuss $f(R)$ theories and chameleonic quantum gravity.
Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power run-away potentials and field independent couplings to matter. In this paper we investigate field-theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thi…
Following work by Khoury and Weltman, we introduce a scalar field phi, the chameleon, which is conformally coupled to matter. That is, matter experiences a metric which is a conformal transform (parametrized by phi) of the Einstein metric. The effective potential of the field phi is a sum of its self-interaction term and an exponential term due to the conformal coupling. Under certain conditions on the self-interaction and the coupling, this effective potential has a minimum which depends on the local matter density, as does its second derivative at the minimum. As a result, the scalar field a…
As a result of non-linear self-interactions, in chameleon theories where the field couples to matter much more strongly than gravity does, the fifth force between two bodies with thin-shell is independent of their coupling to the field. As a consequence the bounds on the coupling coming from terrestrial tests of gravity, measurements of the Casimir force and those constraints imposed by the physics of compact objects, big-bang nucleosynthesis and measurements of the cosmic microwave background anisotropies can be exponentially relaxed.
The chameleon mechanism appearing in massive tensor-scalar theory of gravity can effectively reduce the nonminimal coupling between the scalar field and matter. This mechanism is invoked to reconcile cosmological data requiring introduction of Dark Energy with small-scale stringent constraints on General Relativity. In this communication, we present constraints on this mechanism obtained by a cosmological analysis (based on Supernovae Ia data) and by a Solar System analysis (based on PPN formalism).
Chameleon, environmentally dependent dilaton, and symmetron gravity are three models of modified gravity in which the effects of the additional scalar degree of freedom are screened in dense environments. They have been extensively studied in laboratory, cosmological, and astrophysical contexts. In this paper, we present a preliminary investigation into whether additional constraints can be provided by studying these scalar fields around black holes. By looking at the properties of a static, spherically symmetric black hole, we find that the presence of a non-uniform matter distribution induce…
The paper discusses a particular model of chameleon gravity where the scalar field has an exponential as $V=M^{4}\exp(\frac{αϕ}{M_{pl}})$ and an exponential coupling to the matter density component of the Universe as $ρ_{m}\exp(\frac{βϕ}{M_{pl}})$. We finds the relations between the four (in principle free) parameters of the model and the first five cosmographic parameters (which can be written in terms of the Hubble parameter and its first four derivatives). If such cosmographic parameter are known then the we present the algebraic relations which can be used to derive the free parameters in …
We analyse a spin precession of slow neutrons in the Einstein-Cartan gravity with torsion, chameleon and magnetic field. For the derivation of the Heisenberg equation of motion of the neutron spin we use the effective low-energy potential, derived by Ivanov and Wellenzohn (Phys. Rev. D92, 125004 (2015)) for slow neutrons, coupled to gravitational, chameleon and torsion fields to order 1/m, where m is the neutron mass. In addition to this low-energy interactions we switch on the interaction of slow neutrons with a magnetic field. We show that to linear order approximation with respect to gravit…
Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon $f(R)$ gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the \textsc{aurig…
We analyse f(R) modifications of Einstein's gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the f(R) theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton's law. Fortunately, the existence of a matter dependent mass and a thin shell effect allows one to alleviate these constraints. The thin shell condition also implies strong restrictions on the cosmological dynamics of the f(R) theories. As a consequence, we …
Toward understanding of dark energy, we propose a novel method to directly produce a chameleon particle and force its decay under controlled gas pressure in a laboratory-based experiment. {\it Chameleon gravity}, characterized by its varying mass depending on its environment, could be a source of dark energy, which is predicted in modified gravity. A remarkable finding is a correspondence between the varying mass and a characteristic pressure dependence of a stimulated photon-photon scattering rate in a dilute gas surrounding a focused photon-beam spot. By observing a steep pressure dependence…
One possibility to explain the current accelerated expansion of the universe may be related with the presence of cosmologically evolving scalar whose mass depends on the local matter density (chameleon cosmology). We point out that matter quantum effects in such scalar-tensor theory produce the chameleon scalar field dependent conformal anomaly. Such conformal anomaly adds higher derivative terms to chameleon field equation of motion. As a result, the principal possibility for instabilities appears. These instabilities seem to be irrelevant at small curvature but may become dangerous in the re…
We study the chameleon field dark matter, dubbed \textit{scalaron}, in $F(R)$ gravity in the Big Bang Nucleosynthesis (BBN) epoch. With an $R^{2}$-correction term required to solve the singularity problem for $F(R)$ gravity, we first find that the scalaron dynamics is governed by the $R^{2}$ term and the chameleon mechanism in the early universe, which makes the scalaron physics model-independent regarding the low-energy scale modification. In viable $F(R)$ dark energy models including the $R^{2}$ correction, our analysis suggests the scalaron universally evolves in a way with a bouncing oscil…
Modified theories of gravity provide us with a unique opportunity to generate innovative tests of gravity. In Chameleon f(R) gravity, the gravitational potential differs from the weak-field limit of general relativity (GR) in a mass dependent way. We develop a probe of gravity which compares high mass clusters, where Chameleon effects are weak, to low mass clusters, where the effects can be strong. We utilize the escape velocity edges in the radius/velocity phase space to infer the gravitational potential profiles on scales of 0.3-1 virial radii. We show that the escape edges of low mass clust…
In chameleon $f(R)$-gravity, the fifth force will lead to `upturns' in galaxy rotation curves near the screening radius. The location of the upturn depends on the cosmic background value of the scalar field $f_{R0}$, as well as the mass, size and environment of the galaxy. We search for this signature of modified gravity in the SPARC sample of measured rotation curves, using an MCMC technique to derive constraints on $f_{R0}$. Assuming NFW dark matter haloes and with $f_{R0}$ freely varying for each galaxy, most galaxies prefer $f(R)$ gravity to $Λ$CDM, but there is a large spread of inferred …
We consider the implications of the swampland conjectures on scalar-tensor theories defined in the Einstein frame in which the scalar interaction is screened. We show that chameleon models are not in the swampland provided the coupling to matter is larger than unity and the mass of the scalar field is much larger than the Hubble rate. We apply these conditions to the inverse power law chameleon and the symmetron. We then focus on the dilaton of string theory in the strong coupling limit, as defined in the string frame. We show that solar system tests of gravity imply that viable dilaton models…
We study constraints on f(R) dark energy models from solar system experiments combined with experiments on the violation of equivalence principle. When the mass of an equivalent scalar field degree of freedom is heavy in a region with high density, a spherically symmetric body has a thin-shell so that an effective coupling of the fifth force is suppressed through a chameleon mechanism. We place experimental bounds on the cosmologically viable models recently proposed in literature which have an asymptotic form f(R)=R-lambda R_c [1-(R_c/R)^{2n}] in the regime R >> R_c. From the solar-system con…
Viable modifications of gravity that may produce cosmic acceleration need to be screened in high-density regions such as the Solar System, where general relativity is well tested. Screening mechanisms also prevent strong anomalies in the large-scale structure and limit the constraints that can be inferred on these gravity models from cosmology. We find that by suppressing the contribution of the screened high-density regions in the matter power spectrum, allowing a greater contribution of unscreened low densities, modified gravity models can be more readily discriminated from the concordance c…
Chameleon mechanism appearing in massive tensor-scalar theory of gravity can effectively reduce locally the non-minimal coupling between the scalar field and matter. This mechanism is invoked to reconcile large-scale departures from general relativity (GR), supposedly accounting for cosmic acceleration, to small scales stringent constraints on GR. In this paper, we carefully investigate this framework on cosmological and solar system scales to derive combined constraints on model parameters, notably by performing a non-ambiguous derivation of observables like luminosity distance and local post…
We show that as a result of non-linear self-interactions, scalar field theories that couple to matter much more strongly than gravity are not only viable but could well be detected by a number of future experiments, provided these are properly designed to do so.
We perform high resolution N-body simulations for f(R) gravity based on a self-adaptive particle- mesh code MLAPM. The Chameleon mechanism that recovers General Relativity on small scales is fully taken into account by self-consistently solving the non-linear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function and density profiles, obtained by Oyaizu et al. (Phys.Rev.D 78, 123524, 2008) and Schmidt et al. (Phys.Rev.D 79, 083518, 2009), and extend the resolution up to k~20 h/Mpc for the measurement of t…
The authors of Ref. \cite{1-2}, investigated cosmic evolution in an external interacting model of scalar tensor gravity namely Brans Dicke chameleon scenario. The procedure of this work contains novelties but, it shall be observed from this comment, their report faces three fundamental drawbacks. One of them concerns the energy conservation equation, and the other two flaws are about mathematical mistakes. In the scalar tensor gravity models, a well-known method, in order to obtain conservation equation one must combine Friedmann equations with modified Klein-Gordon equation. But in Ref. \cite…
