Chameleon Models Research Articles

Gravitational couplings in Chameleon models

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, GN, and the propagation of gravitational waves, Ggw. In particular, we revisit the Chameleon screening mechanism without neglecting the time dependence of the galactic environment where local regions are embedded in, and analyze the induced time evolution on GN and Ggw, which can be tested with Lunar Laser Ranging and direct gravitational waves observations. We explicitly show how and why these two couplings generically differ. We also find that due to the particular way the Chameleon screening mechanism works, their time evolutions are highly suppressed in the weak-field non-relativistic approximation.

Swampland and screened modified gravity

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 are not in the swampland. In the future of the Universe, if the low energy description with a single scalar is still valid and the coupling to matter remains finite, we find that the scalar field energy density must vanish for models with the chameleon and symmetron mechanisms. Hence in these models dark energy is only a transient phenomenon. This is not the case for the strongly coupled dilaton, which keeps evolving slowly, leading to a quasi de Sitter space-time.

Constraining the scalar-tensor gravity theories with and without screening mechanisms by combined observations

Screened modified gravity (SMG) and Brans-Dicke (BD) gravity are typical examples of scalar-tensor theories with and without screening mechanisms, which can suppress the scalar field in dense regions. In this paper, we investigate the tests of time-varying gravitational constant $G$, gravitational dipole radiation, and Nordtvedt effect in BD and SMG theories, respectively. We place new constraints on these theories by combining Cassini experiment, lunar laser ranging (LLR) measurements, and pulsar observations from PSRs J1738$+$0333 and J0348$+$0432. We find that screening mechanism has important influence on theoretical constraints. The strongest, second, and weakest constraints on BD are from Cassini, pulsar, and LLR tests, respectively. The most stringent constraint on SMG comes from LLR measurements and improves the previous best constraint by more than seven orders of magnitude. We derive the bounds on the cosmological evolution of the scalar background in these theories using the time variation of $G$. The results of all tests agree well with general relativity (GR) and give more stringent constraints on the deviations from GR. Finally, as an example, we consider the chameleon model and derive the constraints on the model parameters.

Quantum chameleons

We initiate a quantum treatment of chameleonlike particles, deriving classical and quantum forces directly from the path integral. It is found that the quantum force can potentially dominate the classical one by many orders of magnitude. We calculate the quantum chameleon pressure between infinite plates, which is found to interpolate between the Casimir and the integrated Casimir-Polder pressures, respectively in the limits of full screening and no screening. To this end we calculate the chameleon propagator in the presence of an arbitrary number of one-dimensional layers of material. For the E\"ot-Wash experiment, the five-layer propagator is used to take into account the intermediate shielding sheet, and it is found that the presence of the sheet enhances the quantum pressure by two orders of magnitude. As an example of implication, we show that in both the standard chameleon and symmetron models, large and previously unconstrained regions of the parameter space are excluded once the quantum pressure is taken into account.

Prospects for Searching Thermal Effects, Non-Newtonian Gravity and Axion-Like Particles: Cannex Test of the Quantum Vacuum

We consider the Cannex (Casimir And Non-Newtonian force EXperiment) test of the quantum vacuum intended for measuring the gradient of the Casimir pressure between two flat parallel plates at large separations and constraining parameters of the chameleon model of dark energy in cosmology. A modification of the measurement scheme is proposed that allows simultaneous measurements of both the Casimir pressure and its gradient in one experiment. It is shown that with several improvements the Cannex test will be capable to strengthen the constraints on the parameters of the Yukawa-type interaction by up to an order of magnitude over a wide interaction range. The constraints on the coupling constants between nucleons and axion-like particles, which are considered as the most probable constituents of dark matter, could also be strengthened over a region of axion masses from 1 to 100 meV.

What laboratory experiments can teach us about cosmology: A chameleon example

Laboratory experiments can shed light on theories of new physics introduced in order to explain cosmological mysteries, including the nature of dark energy and dark matter. In this article I will focus on one particular example of this, the chameleon model. The chameleon is an example of a theory which could modify gravity on cosmological distance scales, but its non-linear behavior means that it can also be tested with suitably designed laboratory experiments. The aim of this overview is to present recent theoretical developments to the experimental community.

Astrophysical tests of screened modified gravity

Screened modified gravity models evade solar system tests of relativistic gravitation but exhibit novel and interesting effects on scales between the solar system and the Hubble flow: astrophysical scales. In this paper, we review how astrophysical tests using stars, galaxies, and clusters can be used to constrain these theories. We classify screening into three categories: thin-shell (chameleon, symmetron, and dilaton models), Vainshtein screening (e.g. Galileons and Horndeski), and Vainshtein breaking (e.g. beyond Horndeski and DHOST) and discuss the optimal strategy for probing each. In many cases, this is driven by whether a specific category violates the equivalence principles (strong or weak). We summarize the general model-independent bounds on each screening category that have been derived in the literature.

Status Report and first Light from Cannex: Casimir Force Measurements between flat parallel Plates

The Casimir And Non-Newtonian force Experiment(Cannex) was designed to detect Casimir and hypothetical fifth forces between truly parallel plates of cm size, set 10–30 μm apart. With sub-pN sensitivity and large interacting areas, the experiment aims to settle a long-standing question of Casimir physics regarding the role of dissipation at zero frequency in the description of dielectric functions. Active measurement and control of parallelism allows to accurately probe non-standard geometries, such as crossed cylinders or a cylinder opposing a plate. If the designed precision could also be reached in gas at pressures up to 500 mbar,Cannex has been predicted to rule out completely the so-called chameleon model as explanation for dark energy. After a 6-year construction phase, the experiment has reached a first operational prototype state. In the present article, we give an overview of the setup and applied methods, present proofs of principle for key-technologies, and discuss technical hurdles yet to be overcome. Finally, we present first force gradient measurements between parallel plates in the range 6–40 μm.

Equivalence principle in chameleon models

Most theories that predict time and/or space variation of fundamental constants also predict violations of the Weak Equivalence Principle. In 2004 Khoury and Weltman proposed the so called chameleon field arguing that it could help avoiding experimental bounds on the WEP while having a non-trivial cosmological impact. In this paper we revisit the extent to which these expectations continue to hold as we enter the regime of high precision tests. The basis of the study is the development of a new method for computing the force between two massive bodies induced by the chameleon field which takes into account the influence on the field by both, the large and the test bodies. We confirm that in the thin shell regime the force does depend non-trivially on the test body\' s composition, even when the chameleon coupling constants are universal. We also propose a simple criterion based on energy minimization, that we use to determine which of the approximations used in computing the scalar field in a two body problem is better in each specific regime. As an application of our analysis we then compare the resulting differential acceleration of two test bodies with the corresponding bounds obtained from E\"otv\"os type experiments. We consider two setups: 1) an Earth based experiment where the test bodies are made of Be and Al; 2) the Lunar Laser Ranging experiment. We find that for some choices of the free parameters of the chameleon model the predictions of the E\"otv\"os parameter are larger than some of the previous estimates. As a consequence, we put new constrains on these free parameters. An important result of our analysis is that our approach leads to new constraints on the parameter space of the chameleon models.

Noncommutative universe and chameleon field dynamics

We consider a noncommutative standard model with a minimal coupling scalar field and a dynamical deformation between the canonical momenta of its scale factor and scalar field, and a chameleon model with a non-minimally coupling scalar field. We indicate that there is a correspondence between these two models, more specific, actually between the noncommutative parameter and the chameleon coupling strength, and also between the matter density of the chameleon model and the noncommutative geometry. In addition, the analogy constrains the type of the matter field in the chameleon model to be nearly a cosmic string-like during the inflation. Thus, the scenario enables the evolution of the universe being described by one single scalar field. That is, the effects of the chameleon and the inflaton can be described by one single scalar field which plays the role of inflaton in the very early universe and then, acts as a chameleon field. Moreover, the proposed correspondence procedure not only sets some constraints on the noncommutative parameter and the chameleon coupling constant, but also nearly specifies functions of the scalar field and its potential.

Tests of gravity with future space-based experiments

Future space-based tests of relativistic gravitation-laser ranging to Phobos, accelerometers in orbit, and optical networks surrounding Earth-will constrain the theory of gravity with unprecedented precision by testing the inverse-square law, the strong and weak equivalence principles, and the deflection and time-delay of light by massive bodies. In this paper, we estimate the bounds that could be obtained on alternative gravity theories that use screening mechanisms to suppress deviations from general relativity in the solar system: chameleon, symmetron, and galileon models. We find that space-based tests of the parameterized post-Newtonian parameter $\gamma$ will constrain chameleon and symmetron theories to new levels in the solar system, and that tests of the inverse-square law using laser ranging to Phobos will provide the most stringent constraints on galileon theories to date. We end by discussing the potential for constraining these theories using upcoming tests of the weak equivalence principle, and conclude that further theoretical modeling is required in order to fully utilize the data.

Tests of chameleon gravity

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 reinterpreting existing datasets. The results of these searches are often presented using different parametrizations, which can make it difficult to compare constraints coming from different probes. The purpose of this review is to summarize the present state-of-the-art searches for screened scalars coupled to matter, and to translate the current bounds into a single parametrization to survey the state of the models. Presently, commonly studied chameleon models are well-constrained but less commonly studied models have large regions of parameter space that are still viable. Symmetron models are constrained well by astrophysical and laboratory tests, but there is a desert separating the two scales where the model is unconstrained. The coupling of chameleons to photons is tightly constrained but the symmetron coupling has yet to be explored. We also summarize the current bounds on f(R) models that exhibit the chameleon mechanism (Hu and Sawicki models). The simplest of these are well constrained by astrophysical probes, but there are currently few reported bounds for theories with higher powers of R. The review ends by discussing the future prospects for constraining screened modified gravity models further using upcoming and planned experiments.

Chameleon field dynamics during inflation

By studying the chameleon model during inflation, we investigate whether it can be a successful inflationary model, wherein we employ the common typical potential usually used in the literature. Thus, in the context of the slow-roll approximations, we obtain the e-folding number for the model to verify the ability of resolving the problems of standard big bang cosmology. Meanwhile, we apply the constraints on the form of the chosen potential and also on the equation of state parameter coupled to the scalar field. However, the results of the present analysis show that there is not much chance of having the chameleonic inflation. Hence, we suggest that if through some mechanism the chameleon model can be reduced to the standard inflationary model, then it may cover the whole era of the universe from the inflation up to the late time.

Observational constraints on tachyonic chameleon dark energy model

It has been recently shown that tachyonic chameleon model of dark energy in which tachyon scalar field non-minimally coupled to the matter admits stable scaling attractor solution that could give rise to the late-time accelerated expansion of the universe and hence alleviate the coincidence problem. In the present work, we use data from Type Ia supernova (SN Ia) and Baryon Acoustic Oscillations to place constraints on the model parameters. In our analysis we consider in general exponential and non-exponential forms for the non-minimal coupling function and tachyonic potential and show that the scenario is compatible with observations.

Electrostatic analogy for symmetron gravity

The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductors in electrostatics. Based on this analogy we find that the symmetron field exhibits a lightning rod effect wherein the field gradients are enhanced near the ends of pointed or elongated objects. An ellipsoid placed in a uniform symmetron gradient is shown to experience a torque. By symmetry there is no gravitational torque in this case. Hence this effect unmasks the symmetron and might serve as the basis for future laboratory experiments. The symmetron force between a point mass and a large dense body includes a component corresponding to the interaction of the point mass with its image in the larger body. None of these effects have counterparts in the Newtonian limit of Einstein gravity. We discuss the similarities between symmetron gravity and the chameleon model as well as the differences between the two.

Parameterised post-Newtonian expansion in screened regions

The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. Here we incorporate screening mechanisms of modified gravity theories into the framework by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. To determine these functions we develop a general method for efficiently performing the post-Newtonian expansion in screened regimes. For illustration, we derive all the PPN functions for a cubic galileon and a chameleon model. We also analyse the Shapiro time delay effect for these two models and find no deviations from General Relativity insofar as the signal path and the perturbing mass reside in a screened region of space.

More “Critical Mass”, Higher Quality and Visibility of Annalen der Physik

Dear readers, The present regular issue of Annalen der Physik is a perfect example for the successful path that the journal has taken over the past five years: It contains two Rapid Research Letters on soliton transport 1 and aperiodic photonic crystals,2 one Review Article by Pedro David Garcia and Peter Lodahl on quantum photonics,3 and two Feature Articles by Sandro Wimberger et al.4 and David M. Weld et al.5, respectively, on ultracold atoms. These are accompanied by 14 further Original Papers presenting new results in various fields ranging from quantum physics over optics and magnetism to black holes, hence representing a snapshot of today's research and a broad spectrum of current activities in physics. In recent years we have seen a significant uptake in both quantity and quality of submissions, and a higher visibility of published articles as reflected by increased access numbers. Among the current download highlights we find Dmitriy Podolskiy's and stem-cell researcher Robert Lanza's considerations on quantum gravity and the “arrow of time” 6 as well as – no big surprise – the contribution on the physics of the first detected black hole merger by the LIGO/VIRGO collaborations.7 The latter are certainly on the express route to Stockholm now after the third gravitational wave detection – we have our fingers crossed for this year's Nobel Prize in Physics! More hot topics to feature in AdP are concerned with many-body localization 8 and – the soon to come – physics and technology of graphene,9 now a large-scale research endeavor in Europe and world-wide. Last but certainly not least, this positive development has also led to higher citation numbers and an increased Impact Factor now stably ranging above 3. The 2016 Impact Factor is 3.039, with an Immediacy Index (citations already within the year of publication) boosted by 36% to 0.964. Top-cited contributions since 2014 are Review Articles on quantum optics in chiral conductors,10 chameleon models for cosmology 11 and transition metal dichalcogenides,12 followed by topics such as super-resolution microscopy and high-temperature superconductivity. Annalen der Physik is now among the five best-cited journals publishing original research in general physics. All this would not be possible without you, our authors, numerous peer-reviewers, and readers, hence a growing community of contributors and supporters of our flagship Annalen der Physik. We are confident that this upward trend of more relevant “critical mass” in the journal will continue in the years to come. Stefan Hildebrandt Editor-in-Chief Several articles in this and forthcoming issues of the journal have been invited by our former author 13 Regine Frank, Bonn, and are partly related to the Europhysics Conference “From Photonics to Polaritonics – Non-Equilibrium Transport, Complex Media, Photonic Crystals and Disordered Nano-Structures” that took place in Les Houches in 2016. Her activities and the contributions from workshop presenters are gratefully acknowledged.

Extrasolar planets as a probe of modified gravity

We propose a new method to test modified gravity theories, taking advantage of the available data on extrasolar planets. We computed the deviations from the Kepler third law and use that to constrain gravity theories beyond General Relativity. We investigate gravity models which incorporate three screening mechanisms: the Chameleon, the Symmetron and the Vainshtein. We find that data from exoplanets orbits are very sensitive to the screening mechanisms putting strong constraints in the parameter space for the Chameleon models and the Symmetron, complementary and competitive to other methods, like interferometers and solar system. With the constraints on Vainshtein we are able to work beyond the hypothesis that the crossover scale is of the same order of magnitude than the Hubble radius rc∼H0−1, which makes the screening work automatically, testing how strong this hypothesis is and the viability of other scales.

A compendium of chameleon constraints

The chameleon model is a scalar field theory with a screening mechanism that explains how a cosmologically relevant light scalar can avoid the constraints of intra-solar-system searches for fifth-forces. The chameleon is a popular dark energy candidate and also arises in f(R) theories of gravity. Whilst the chameleon is designed to avoid historical searches for fifth-forces it is not unobservable and much effort has gone into identifying the best observables and experiments to detect it. These results are not always presented for the same models or in the same language, a particular problem when comparing astrophysical and laboratory searches making it difficult to understand what regions of parameter space remain. Here we present combined constraints on the chameleon model from astrophysical and laboratory searches for the first time and identify the remaining windows of parameter space. We discuss the implications for cosmological chameleon searches and future small-scale probes.

Finding Horndeski theories with Einstein gravity limits

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 not. For this purpose, we develop a new and surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.