Chameleon Models Research Articles

Dynamical Casimir effect with screened scalar fields

Understanding the nature of dark energy and dark matter is one of modern physics' greatest open problems. Scalar-tensor theories with screened scalar fields like the chameleon model are among the most popular proposed solutions. In this article, we present the first analysis of the impact of a chameleon field on the dynamical Casimir effect, whose main feature is the particle production associated with a resonant condition of boundary periodic motion in cavities. For this, we employ a recently developed method to compute the evolution of confined quantum scalar fields in a globally hyperbolic spacetime by means of time-dependent Bogoliubov transformations. As a result, we show that particle production is reduced due to the presence of the chameleon field. In addition, our results for the Bogoliubov coefficients and the mean number of created particles agree with known results in the absence of a chameleon field. Our results initiate the discussion of the evolution of quantum fields on screened scalar field backgrounds.

Stability analysis of the cosmological dynamics of O(D, D)-complete stringy gravity

The massless fields in the universal NS-NS sector of string theory form O(D, D) multiplets of Double Field Theory, which is a theory that provides a T-duality covariant formulation of supergravity, leading to a stringy modification of General Relativity. In this framework, it is possible to write down the extensions of the Einstein field equations and the Friedmann equations in such a way that the coupling of gravitational and matter sectors is dictated by the O(D, D) symmetry universally. In this paper, we obtain the autonomous form of the O(D, D)-complete Friedmann equations, find the critical points and perform their stability analysis. We also include the phase portraits of the system. Cosmologically interesting cases of scalar field, radiation, and matter are separately considered and compared with the Chameleon models in a similar setting. Accelerating phases and the conditions for their existence are also given for such cases.

Axio-Chameleons: a novel string-friendly multi-field screening mechanism

Scalar-tensor theories with the shift symmetries required by light scalars are well-explored modifications to GR. For these, two-derivative scalar self-interactions usually dominate at low energies and interestingly compete with the two-derivative metric interactions of GR itself. Although much effort has been invested in single scalars (on grounds of simplicity) these happen to have no two-derivative interactions, requiring such models to explore higher-derivative interactions (that usually would be less important at low-energies). This suggests multiple-scalar sigma models as well-motivated candidates for finding new phenomena in tests of gravity. We identify a new multi-field screening mechanism appropriate for two light scalar fields (an axion and a Brans-Dicke style dilaton) that relies on their mutual two-derivative interactions. We show how very weak axion-matter couplings can introduce axion gradients that can reduce the apparent coupling of the Brans-Dicke scalar to macroscopic matter sources. We further identify a relaxation mechanism that allows this reduction to be amplified to a suppression by the ratio of the axion gradient's length scale to the source's radius (similar in size to the suppression found in Chameleon models). Unlike some screening mechanisms our proposal is technically natural and works deep within the regime of control of the low-energy EFT. It uses only ingredients that commonly appear in the low-energy limit of string vacua and so is likely to have wider applications to models that admit UV completions. We briefly discuss phenomenological implications and challenges for this scenario, which suggests re-examination of decay loss bounds and the value of equivalence-principle tests for different-sized objects.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

Neutrino flavor oscillations inside matter in conformal coupling models

We recently studied neutrinos flavor oscillations in vacuum within conformal coupling models. In this paper, we extend that analysis by investigating neutrino flavor oscillations inside matter within a general conformal coupling scenario. We first derive the general formula for the flavor transition probability inside matter in arbitrary static and spherically symmetric spacetimes. The modified resonance formula of the MSW effect is derived and the corresponding adiabaticity parameter of the effect is extracted. An application of our results to the case of two-flavor neutrinos within the well-known chameleon and symmetron conformal coupling models is made.

Casimir tests of scalar-tensor theories

We compute bounds and forecasts on screened modified gravity theories, specialising to the chameleon model in Casimir force experiments. In particular, we investigate the classical interaction between a plate and sphere subject to a screened interaction of the chameleon type. We compare numerical simulations of the field profile and the classical pressure exerted on the sphere to analytical approximations for these non-linear field theories. In particular, we focus on the proximity force approximation (PFA) and show that, within the range of sphere sizes $R$ and plate-sphere distance $D$ simulated numerically, the PFA does not reproduce the numerical results. This differs from the case of linear field theories such as Newtonian gravity and a Yukawa model where the PFA coincides with the exact results. We show that for chameleon theories, the screening factor approximation (SFA) whereby the sphere is modelled as a screened sphere embedded in the external field due to the plates, fares better and can be used in the regime $D\gtrsim R$ to extract constraints and forecasts from existing and forthcoming data. In particular, we forecast that future Casimir experiments would corroborate the closing of the parameter space for the simplest of chameleon models at the dark energy scale.

Screened scalar fields in hydrogen and muonium

We compute bounds on screened scalar field theories from hydrogen-like systems. New light scalar fields generically have a direct coupling to matter. Such a coupling is strongly constrained by myriad experimental measurements. However, certain theories possess a {\it screening mechanism} that allows the effects of this coupling to weaken dynamically, and to evade many such bounds. We compute the perturbations to the energy levels of hydrogen-like systems due to screened scalar fields. We then use this result in two ways. First, we compute bounds from hydrogen spectroscopy, finding significantly weaker bounds than have been reported before as screening effects were overlooked. Second, we show that muonium is an intrinsically much more sensitive probe of screened scalar fields. For chameleon models, muonium experiments probe a large part of the parameter space that is as yet unexplored by low energy physics and has so far only been tested by high-energy particle physics experiments.

Solving nonlinear Klein-Gordon equations on unbounded domains via the finite element method

A large class of scalar-tensor theories of gravity exhibit a screening mechanism that dynamically suppresses fifth forces in the Solar system and local laboratory experiments. Technically, at the scalar field equation level, this usually translates into nonlinearities which strongly limit the scope of analytical approaches. This article presents $femtoscope$ $-$ a Python numerical tool based on the Finite Element Method (FEM) and Newton method for solving Klein-Gordon-like equations that arise in particular in the symmetron or chameleon models. Regarding the latter, the scalar field behavior is generally only known infinitely far away from the its sources. We thus investigate existing and new FEM-based techniques for dealing with asymptotic boundary conditions on finite-memory computers, whose convergence are assessed. Finally, $femtoscope$ is showcased with a study of the chameleon fifth force in Earth orbit.

Chameleon screening in cosmic voids

A key goal in cosmology in the upcoming decade will be to form a better understanding of the accelerated expansion of the Universe. Upcoming surveys, such as the Vera C. Rubin Observatory's 10-year Legacy Survey of Space and Time (LSST), Euclid and the Square Killometer Array (SKA) will deliver key datasets required to tackle this and other puzzles in contemporary cosmology. With this data, constraints of unprecedented power will be put on different models of dark energy and modified gravity. In this context it is crucial to understand how screening mechanisms, which hide the deviations of these theories from the predictions of general relativity in local experiments, affect structure formation. In this work we approach this problem by using a combination of analytic and numerical methods to describe chameleon screening in the context of cosmic voids. We apply a finite element method (FEM) code, SELCIE, to solve the chameleon equation of motion for a number of void profiles derived from observational data and simulations. The obtained results indicate a complex relationship between the properties of cosmic voids and the size of the chameleon acceleration of a test particle. We find that the fifth force on a test particle in a void is primarily related to the depth and the inner density gradient of the void. For realistic void profiles, the obtained chameleon-to-Newtonian acceleration ratios range between aϕ /aNewt ≈ 10-6– 10-5. However, it should be noted that in unusually deep voids with large inner density gradients, the acceleration ratios can be significantly higher. Similarly, other chameleon models, such as f(R) Hu-Sawicki theory allow for significantly higher acceleration ratios. Given these results, we also discuss the optimal density profiles for detecting the fifth force in the upcoming observational surveys.

Searching for Chameleon Dark Energy with Mechanical Systems.

A light scalar field framework of dark energy, sometimes referred to as quintessence, introduces a fifth force between normal matter objects. Screening mechanisms, such as the chameleon model, allow the scalar field to be almost massless on cosmological scales while simultaneously evading laboratory constraints. We explore the ability of existing mechanical systems to directly detect the fifth force associated with chameleons in an astrophysically viable regime where it could be dark energy. We provide analytical expressions for the weakest accessible chameleon model parameters in terms of experimentally tunable variables and apply our analysis to two mechanical systems: levitated microspheres and torsion balances, showing that the current generation of these experiments have the sensitivity to rule out a significant portion of the proposed chameleon parameter space. We also indicate regions of theoretically well-motivated chameleon parameter space to guide future experimental work.

Cosmic acceleration and geodesic deviation in chameleon scalar field model

While considering the chameleon scalar field model with the spatially flat FLRW background, we investigate the late-time acceleration phase of the universe, wherein we apply the typical potential usually used in this model. Through setting some constraints on the free parameters of the model, we indicate that the non-minimal coupling between the matter and the scalar field in such a model should be strongly coupled in order to have an accelerated expansion of the universe at the late-time. We also investigate the relative acceleration of the parallel geodesics by obtaining the geodesic deviation equation in the context of chameleon model. Then, through the null deviation vector fields, we obtain the observer area-distance as a measurable quantity to compare the model with other relevant models.

Hunting dark energy with pressure-dependent photon-photon scattering

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. 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 in the scattering rate, we can directly extract the characteristic feature of the chameleon mechanism. As a benchmark model of modified gravity consistent with the present cosmological observations, a reduced $F(R)$ gravity is introduced in the laboratory scale. We then demonstrate that the proposed method indeed enables a wide-ranging parameter scan of such a chameleon model with the varying mass around $(0.1\ensuremath{-}1)\text{ }\text{ }(\ensuremath{\mu}\mathrm{eV})$ by controlling pressure values.

Chameleon screening depends on the shape and structure of NFW halos

Chameleon gravity is an example of a model that gives rise to interesting phenomenology on cosmological scales while simultaneously possessing a screening mechanism, allowing it to avoid solar system constraints. Such models result in non-linear field equations, which can be solved analytically only in simple highly symmetric systems. In this work we study the equation of motion of a scalar-tensor theory with chameleon screening using the finite element method. More specifically, we solve the field equation for spherical and triaxial NFW cluster-sized halos. This allows a detailed investigation of the relationship between the NFW concentration and the virial mass parameters and the magnitude of the chameleon acceleration, as measured at the virial radius. In addition, we investigate the effects on the chameleon acceleration due to halo triaxiality. We focus on the parameter space regions that are still allowed by the observational constraints. We find that given our dataset, the largest allowed value for the chameleon-to-NFW acceleration ratio at the virial radius is ∼ 10-7. This result strongly indicates that the chameleon models that are still allowed by the observational constraints would not lead to any measurable effects on galaxy cluster scales. Nonetheless, we also find that there is a direct relationship between the NFW potential and the chameleon-to-NFW acceleration ratio at the virial radius. Similarly, there is a direct (yet a much more complicated) relationship between the NFW concentration, the virial mass and the acceleration ratios at the virial radius. Finally, we find that triaxiality introduces extra directional effects on the acceleration measurements. These effects in combination could potentially be used in future observational searches for fifth forces.

SELCIE: a tool for investigating the chameleon field of arbitrary sources

The chameleon model is a modified gravity theory that introduces an additional scalar field that couples to matter through a conformal coupling. This `chameleon field' possesses a screening mechanism through a nonlinear self-interaction term which allows the field to affect cosmological observables in diffuse environments whilst still being consistent with current local experimental constraints. Due to the self-interaction term the equations of motion of the field are nonlinear and therefore difficult to solve analytically. The analytic solutions that do exist in the literature are either approximate solutions and or only apply to highly symmetric systems. In this work we introduce the software package SELCIE (https://github.com/C-Briddon/SELCIE.git). This package equips the user with tools to construct an arbitrary system of mass distributions and then to calculate the corresponding solution to the chameleon field equation. It accomplishes this by using the finite element method and either the Picard or Newton nonlinear solving methods. We compared the results produced by SELCIE with analytic results from the literature including discrete and continuous density distributions. We found strong (sub-percentage) agreement between the solutions calculated by SELCIE and the analytic solutions.

Biomimetic chameleon soft robot with artificial crypsis and disruptive coloration skin

Development of an artificial camouflage at a complete device level remains a vastly challenging task, especially under the aim of achieving more advanced and natural camouflage characteristics via high-resolution camouflage patterns. Our strategy is to integrate a thermochromic liquid crystal layer with the vertically stacked, patterned silver nanowire heaters in a multilayer structure to overcome the limitations of the conventional lateral pixelated scheme through the superposition of the heater-induced temperature profiles. At the same time, the weaknesses of thermochromic camouflage schemes are resolved in this study by utilizing the temperature-dependent resistance of the silver nanowire network as the process variable of the active control system. Combined with the active control system and sensing units, the complete device chameleon model successfully retrieves the local background color and matches its surface color instantaneously with natural transition characteristics to be a competent option for a next-generation artificial camouflage.

Non-canonical Chameleon cosmology

One of the most important issues in modern cosmology is understanding the origin of the accelerated expansion of the universe, known as “dark energy”. The scalar–tensor model is one of the most interesting candidates for describing dark energy. In this paper, we investigate the non-canonical scalar model, which is written in the framework of Chameleon models. In this model, the scalar field is coupled to a mass density [Formula: see text] under an arbitrary [Formula: see text] coupling function. We study the cosmological aspect of this model according to its Chameleon state and we conclude that for high densities, the mass of the Chameleon field becomes larger, so its effect will not be seen in high-density areas. We also examine the dynamical behavior of this model for different coupling functions and potentials. According to the dynamic behavior of the model, we can conclude that using this model can explain the accelerated expansion of the universe. Finally, we investigate the tensor perturbations in this model and show that the mass of the gravitational waves obtained in the framework of this model can be in good agreement with the observations.

Constraining the chameleon model with the HUST-2020 torsion pendulum experiment

The chameleon model was proposed as a promising candidate for the dark energy screening mechanism. It is not straightforward to detect the fifth force mediated by the chameleon scalar field in a high-density environment, such as those in a ground-based laboratory. Nevertheless, short-range gravitational experiments such as the torsion pendulum experiment can provide strong constraints on the chameleon model. In this work, we constrain the chameleon model from a precise test of the inverse-square law at Huazhong University of Science and Technology. In particular, we take full advantage of the regular flat-plate structure of the test and attraction mass, which gives rise to accurate modeling for the chameleon force and torque. The derived analytical results on the chameleon torque are shown to agree well with those by numerical calculations. Subsequently, based on the experimental data, the parameter space of the chameleon model is analyzed, and the results are presented in terms of a more stringent constraint on the model parameters.

Are Type Ia supernova powerful tool to detect anisotropic expansion of the Universe?

In this paper, we present a detailed analysis of the dark energy dipole using Union2, Pantheon and GRB dataset in Chameleon and Teleparallel dark energy models, in comparison with Lambda CDM. Both models are extensively studied in recent years and our result shows that with Union2 and Pantheon data, the preferred direction of the anisotropy in both models are very close to each other as well as with those obtained in some studies for Lambda CDM. However, when the models fitted with a combination of Union 2 and GRB, the statistical analysis slightly favors the Chameleon cosmology over Teleparallel gravity, with the maximum anisotropic direction of (l = 330^{+30}_{-28}, b = -15^{+23}_{-25}) in galactic coordinate system, comparable with alpha -dipole result in Keck-VLT data and LCDM.

Highly compact neutron stars and screening mechanisms: Equilibrium and stability

Modified theories of gravity that offer viable models for dark energy often rely on mechanisms that screen their effects in high density environments. From this perspective, it would appear that, once solar system constraints are satisfied, these theories would predict a trivial phenomenology for (much denser) neutron stars. In this work we explore the fact that in scalar-tensor theories the scalar degree of freedom does not couple to the mass density alone, but to the trace of the energy-momentum tensor - which can increase and eventually change sign as density and pressure build up in the core of neutron stars -, and investigate whether there could be a partial unscreening of the scalar field inside the most compact stars found in Nature. For this purpose, we construct neutron star solutions with realistic equations of state in theories with screening mechanisms and study their stability under radial perturbations. In particular, we find that stable solutions with a unscreened core can exist in chameleon models, while for the environmentally-dependent dilaton model a wealth of new, scalarized equilibrium solutions are found, some of which can be stable.

Constraining the cosmological evolution of scalar-tensor theories with local measurements of the time variation of G

We determine the conditions for which the constraints from lunar laser ranging on the time evolution of the local gravitational constant can be extrapolated to impose constraints on the time evolution of the cosmological gravitational constant in scalar-tensor theories of modified gravity. We allow for the possibility that the scalar-tensor theories are non-linear and contain a screening mechanism. This results in strong late Universe constraints on the running of the cosmological Planck mass described by the Horndeski function |αM|≲ 0.002. We find that our assumptions are valid for most Vainshtein and kinetic screening models, where the shift symmetry ϕ→ϕ + c holds, but are violated by some Chameleon and Symmetron screening models, where the macroscopic equivalence principle is broken.