Symmetron Model Research Articles

On validity of the quasi-static approximation in scalar-tensor theories

The discovery of cosmic acceleration motivated extensive studies of dynamical dark energy and modified gravity models. Of particular interest are the scalar-tensor theories, with a scalar field dark energy non-minimally coupled to matter. Cosmological constraints on these models often employ the quasi-static approximation (QSA), in which the dynamics of the scalar field perturbations is proportional to the perturbation in the matter density. Using the QSA simplifies the physical interpretation of the phenomenology of scalar-tensor theories, and results in substantial savings of computing time when deriving parameter constraints. Focusing on the symmetron model, which is a well-motivated scalar-tensor theory with a screening mechanism, we compare the exact solution of the linearly perturbed field equations to those obtained under the QSA and identify the range of the model parameters for which the QSA is valid. We find that the evolution of background scalar field is most important, namely, whether it is dominated by the Hubble friction or the scalar field potential. This helps us derive a criterion for the symmetron model, but same argument can be applied to other scalar-tensor theories of generalized Brans-Dicke type. We consider two scenarios, one where the scalar field is only coupled to dark matter and where it couples to all of the matter.

Lensing with Generalized Symmetrons

Generalized symmetrons are models that have qualitatively similar features to the archetypal symmetron, but have barely been studied. In this article, we investigate for what parameter values the fifth forces induced by disformally coupling generalized symmetrons can provide an explanation for the difference between baryonic and lens masses of galaxies. While it is known that the standard symmetron struggles to provide an alternative source for the lensing otherwise attributed to particle dark matter, we show that some generalized symmetron models are more suitable for complying with existing constraints on disformal couplings. This motivates future studies of these only little-explored models.

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.

Constraining the Symmetron Model with the HUST-2020 Torsion Pendulum Experiment.

The search for dynamically screening the coupling between the scalar field and matter in high-density environment is achievable with the symmetron model. The high-accuracy and short-range gravity experiment is proposed to test the symmetron model. In this Letter, the data of the HUST-2020 torsion pendulum experiment testing the inverse-square law at submillimeter range is analyzed to constrain the symmetron model. The results show that the HUST-2020 experiment is uniquely sensitive to probe the symmetron model with a mass scale of μ=7.2×10^{-3} eV, and the self-coupling parameter λ≲105 is excluded at mass scale M=0.3 TeV. Especially, at the dark energy scale μ=2.4×10^{-3} eV, the constraint at M=1.3 TeV is improved by about 10 times the previous constraints on the torsion pendulum experiment.

Superradiant instabilities by accretion disks in scalar-tensor theories

We study the superradiant instability in scalar-tensor theories of gravitation, where matter outside a black hole provides an effective mass to the scalar degree of freedom of the gravitational sector. We discuss this effect for arbitrarily spinning black holes and for realistic models of truncated thin and thick accretion disks (where the perturbation equations are nonseparable), paying particular attention to the role of hot coronal flows in the vicinity of the black hole. The system qualitatively resembles the phenomenology of plasma-driven superradiant instabilities in general relativity. Nevertheless, we show that the obstacles hampering the efficiency of plasma-driven superradiant instabilities in general relativity can be circumvented in scalar-tensor theories. We find a wide range of parameter space where superradiant instabilities can be triggered in realistic scenarios, and discuss the constraints on scalar-tensor theories imposed by this effect. In particular, we argue that the existence of highly spinning accreting black holes is in tension with some scalar-tensor alternatives to the dark energy, e.g., symmetron models with screening.

Fast full N-body simulations of generic modified gravity: derivative coupling models

We present mg-glam, a code developed for the very fast production of full N-body cosmological simulations in modified gravity (MG) models. We describe the implementation, numerical tests and first results of a large suite of cosmological simulations for two broad classes of MG models with derivative coupling terms — the Vainshtein- and Kmouflage-type models — which respectively features the Vainshtein and Kmouflage screening mechanism. Derived from the parallel particle-mesh code glam, mg-glam incorporates an efficient multigrid relaxation technique to solve the characteristic nonlinear partial differential equations of these models. For Kmouflage, we have proposed a new algorithm for the relaxation solver, and run the first simulations of the model to understand its cosmological behaviour. In a companion paper, we describe versions of this code developed for conformally-coupled MG models, including several variants of f(R) gravity, the symmetron model and coupled quintessence. Altogether, mg-glam has so far implemented the prototypes for most MG models of interest, and is broad and versatile. The code is highly optimised, with a tremendous (over two orders of magnitude) speedup when comparing its running time with earlier N-body codes, while still giving accurate predictions of the matter power spectrum and dark matter halo abundance. mg-glam is ideal for the generation of large numbers of MG simulations that can be used in the construction of mock galaxy catalogues and accurate emulators for ongoing and future galaxy surveys.

Neutron Stars in the Symmetron Model

Screening mechanisms are often deployed by dark energy models to conceal the effects of their new degrees of freedom from the scrutiny of terrestrial and solar system experiments. However, the extreme properties of nuclear matter may lead to a partial failure of screening mechanisms inside the most massive neutron stars observed in nature, opening up the possibility of probing these theories with neutron star observations. In this work, we explore equilibrium and stability properties of neutron stars in two variants of the symmetron model. We show that around sufficiently compact neutron stars, the symmetron is amplified with respect to its background (cosmological) value by several orders of magnitude, and that the properties of such unscreened stars are sensitive to corrections to the leading linear coupling between the symmetron and matter.

New bounds on macroscopic scalar-field topological defects from nontransient signatures due to environmental dependence and spatial variations of the fundamental constants

We point out that in models of macroscopic topological defects composed of one or more scalar fields that interact with standard model fields via scalar-type couplings the back action of ambient matter on the scalar field(s) produces an environmental dependence of the fundamental constants of nature as well as spatial variations of the fundamental constants in the vicinity of dense bodies such as Earth due to the formation of a ``bubblelike'' defect structure surrounding the dense body. In sufficiently dense environments, spontaneous symmetry breaking may be inhibited altogether for ${\ensuremath{\phi}}^{2}$ interactions, potentially delaying the cosmological production of topological defects to rather late times. We derive bounds on nontransient variations of the fundamental constants from torsion-pendulum experiments that search for equivalence-principle-violating forces, experiments comparing the frequencies of ground- and space-based atomic clocks as well as ground-based clocks at different heights in the recent Tokyo Skytree experiment, and measurements comparing atomic and molecular transition frequencies in terrestrial and low-density astrophysical environments. Our results constrain the present-day mass-energy fraction of the Universe due to a network of infinite domain walls produced shortly after the big bang nucleosynthesis or cosmic microwave background epochs to be ${\mathrm{\ensuremath{\Omega}}}_{\text{walls},0}\ensuremath{\ll}{10}^{\ensuremath{-}10}$ for the symmetron model with a ${\ensuremath{\phi}}^{4}$ potential and ${\ensuremath{\phi}}^{2}$ interactions, improving over cosmic microwave background quadrupolar temperature anisotropy bounds by at least 5 orders of magnitude. Our newly derived bounds on domain walls with ${\ensuremath{\phi}}^{2}$ interactions via their effects of nontransient variations of the fundamental constants are significantly more stringent than previously reported clock- and cavity-based limits on passing domain walls via transient signatures (regardless of their possible degradation due to previously neglected effects of the strongly repulsive potential generated by Earth on the passing domain walls) and previous bounds from different types of nontransient signatures (by about 10 orders of magnitude for wall thicknesses comparable to the size of Earth), under the same set of assumptions.

The two body problem in the presence of dark energy and modified gravity: application to the Local Group

We explore mass estimation of the Local Group via the use of the simple, dynamical `timing argument' in the context of a variety of theories of dark energy and modified gravity: a cosmological constant, a perfect fluid with constant equation of state w, quintessence (minimally coupled scalar field), MOND, and symmetrons (coupled scalar field). We explore generic coupled scalar field theories, with the symmetron model as an explicit example. We find that theories which attempt to eliminate dark matter by fitting rotation curves produce mass estimates in the timing argument which are not compatible with the luminous mass of the galaxies alone. Assuming that the galaxies are approaching their first encounter, MOND gives a mass of around 2.7× 1010 M⊙, roughly 10% of the luminous mass of the LG, although a higher mass can be obtained in the case of a previous fly-by event between the MW and M31. The symmetron model suggests a mass too high to be explained without additional dark matter (\U0001d4aa(1012) M⊙), suggesting that there is a missing mass problem in this model. We also demonstrate that tensions in measurements of H0 can produce an uncertainty in the Local Group mass estimate comparable to observational uncertainties on the separation and relative velocity of the galaxies, with values for the mass ranging from 4.4–5.3 × 1012 M⊙ varying h between 0.63 and 0.76.

Mass-temperature relation in ΛCDM and modified gravity

We derive the mass-temperature relation using an improved top-hat model and a continuous formation model which takes into account the effects of the ordered angular momentum acquired through tidal-torque interaction between clusters, random angular momentum, dynamical friction, and modifications of the virial theorem to include an external pressure term usually neglected. We show that the mass-temperature relation differs from the classical self-similar behavior, $M \propto T^{3/2}$, and shows a break at $3--4$ keV, and a steepening with a decreasing cluster temperature. We then compare our mass-temperature relation with those obtained in the literature with $N$-body simulations for $f(R)$ and symmetron models. We find that the mass-temperature relation is not a good probe to test gravity theories beyond Einstein's general relativity, because the mass-temperature relation of the $\Lambda$CDM model is similar to that of the modified gravity theories.

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.

Screenings in modified gravity: a perturbative approach

We present a formalism to study screening mechanisms in modified theories of gravity through perturbative methods in different cosmological scenarios. We consider Einstein-frame posed theories that are recast as Jordan-frame theories, where a known formalism is employed, although the resulting nonlinearities of the Klein–Gordon equation acquire an explicit coupling between matter and the scalar field, which is absent in Jordan-frame theories. The obtained growth functions are then separated into screening and non-screened contributions to facilitate their analysis. This allows us to compare several theoretical models and to recognize patterns that can be used to distinguish models and their screening mechanisms. In particular, we find anti-screening features in the symmetron model. In contrast, chameleon-type theories in both the Jordan and Einstein frames always present a screening behaviour. Up to third order in perturbation, we find no anti-screening behaviour in theories with a Vainshtein mechanism, such as the Dvali Gabadadze Porrati braneworld model and the cubic Galileon.

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.

Probing modified gravity in cosmic filaments

Multiple modifications of general relativity (GR) have been proposed in the literature in order to understand the nature of the accelerated expansion of the Universe. However, thus far all the predictions of GR have been confirmed with constantly increasing accuracy. In this work, we study the imprints of a particular class of models – “screened” modified gravity theories – on cosmic filaments. We have utilized the N-body code ISIS/RAMSES to simulate the symmetron model and the Hu–Sawicky f(R) model, and we post-process the output with DisPerSE to identify the filaments of the cosmic web. We investigated how the global properties of the filaments – such as their lengths, masses, and thicknesses – as well as their radial density and speed profiles change under different gravity theories. We find that filaments are, on average, shorter and denser in modified gravity models compared to in ΛCDM. We also find that the speed profiles of the filaments are enhanced, consistent with theoretical expectations. Overall, our results suggest that cosmic filaments can be an effective complementary probe of screened modified gravity theories on Mpc scales.

Degeneracies between modified gravity and baryonic physics

In order to determine the observable signatures of modified gravity theories, it is important to consider the effect of baryonic physics. We used a modified version of the ISIS code to run cosmological hydrodynamic simulations in order to study degeneracies between modified gravity and radiative hydrodynamic processes. One of the simulations was the standard Λ cold dark matter model and four were variations of the Symmetron model. For each model we ran three variations of baryonic processes: nonradiative hydrodynamics; cooling and star formation; and cooling, star formation, and supernova feedback. We constructed stacked gas density, temperature, and dark matter density profiles of the halos in the simulations, and studied the differences between them. We find that both radiative variations of the models show degeneracies between their processes and at least two of the three parameters defining the Symmetron model.

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.

Testing modified gravity with globular clusters: the case of NGC 2419

Abstract The dynamics of globular clusters has been studied in great detail in the context of general relativity as well as with modifications of gravity that strongly depart from the standard paradigm such as Modified Newtonian Dynamics. However, at present there are no studies that aim to test the impact that less extreme modifications of gravity (e.g. models constructed as alternatives to dark energy) have on the behaviour of globular clusters. This Letter presents fits to the velocity dispersion profile of the cluster NGC 2419 under the symmetron-modified gravity model. The data show an increase in the velocity dispersion towards the centre of the cluster which could be difficult to explain within general relativity. By finding the best-fitting solution associated with the symmetron model, we show that this tension does not exist in modified gravity. However, the best-fitting parameters give a model that is inconsistent with the dynamics of the Solar system. Exploration of different screening mechanisms should give us the chance to understand if it is possible to maintain the appealing properties of the symmetron model when it comes to globular clusters and at the same time recover the Solar system dynamics properly.

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.

Unscreening scalarons with a black hole

It is typically believed that the additional degrees of freedom in any modification of gravity are completely suppressed by the large energy densities coexisting with an astrophysical black hole. In this paper, we find that this might not always be the case. This belief holds for black holes formed via gravitational collapse in very dense environments, whereas the black holes with sufficiently low accretion rates that have low matter densities inside innermost stable circular orbit will generally unscreen chameleons. We develop a novel technique to study the dynamics of accretion of a scalar field onto a Schwarzschild-like black hole which is accurate on both short and long time scales. In particular, we study the behavior of the extra scalar degree of freedom in the Starobinsky and Hu-Sawicki $f(R)$ theories, for the symmetron model, and for the Ratra-Peebles model. Aside from calculating non-trivial static field profiles outside the black hole, we provide the tools to study the (in)stability and evolution towards the equilibrium solution for any generic well behaved set of parameters and initial conditions. Our code is made publicly available for further research and modifications to study other models.