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Register a new userThe shape dependence of chameleon screening
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Chameleon scalar fields can screen their associated fifth forces from detection by changing their mass with the local density. These models are an archetypal example of a screening mechanism, and have become an important target for both cosmological surveys and terrestrial experiments. In particular there has been much recent interest in searching for chameleon fifth forces in the laboratory. It is known that the chameleon force is less screened around non-spherical sources, but only the field profiles around a few simple shapes are known analytically. In this work we introduce a numerical code that solves for the chameleon field around arbitrary shapes with azimuthal symmetry placed in a spherical vacuum chamber. We find that deviations from spherical symmetry can increase the chameleon acceleration experienced by a test particle by up to a factor of $sim 3$, and that the least screened objects are those which minimize some internal dimension.
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One of the most pressing questions in modified gravity is how deviations from general relativity can manifest in upcoming galaxy surveys. This is especially relevant for theories exhibiting Vainshtein screening, where such deviations are efficiently suppressed within a (typically large) Vainshtein radius. However, Vainshtein screening is known to be shape dependent: it is most effective around spherical sources, weaker around cylindrical objects and completely absent for planar sources. The Cosmic Web therefore offers a testing ground, as it displays many shapes in the form of clusters, filaments and walls. In this work, we explicitly derive the signature of the shape dependence of Vainshtein screening on the matter bispectrum, by considering a cubic Galileon model with a conformal coupling to matter and a cosmological constant. We perform a second order perturbative analysis, deriving analytic, integral expressions for the bispectrum, which we integrate using hi_class. We find that the shape dependence of Vainshtein screening enters the bispectrum with a unique scale-factor dependence of $propto a^{3/2}$. The magnitude of the effect today is up to 2 % for a model whose linear growth rate deviates up to 5 % from $Lambda$CDM.
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 $sim 10^{-7}$. 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.
We analyse modelling techniques for the large-scale structure formed in scalar-tensor theories of constant Brans-Dicke parameter which match the concordance model background expansion history and produce a chameleon suppression of the gravitational modification in high-density regions. Thereby, we use a mass and environment dependent chameleon spherical collapse model, the Sheth-Tormen halo mass function and linear halo bias, the Navarro-Frenk-White halo density profile, and the halo model. Furthermore, using the spherical collapse model, we extrapolate a chameleon mass-concentration scaling relation from a LCDM prescription calibrated to N-body simulations. We also provide constraints on the model parameters to ensure viability on local scales. We test our description of the halo mass function and nonlinear matter power spectrum against the respective observables extracted from large-volume and high-resolution N-body simulations in the limiting case of f(R) gravity, corresponding to a vanishing Brans-Dicke parameter. We find good agreement between the two; the halo model provides a good qualitative description of the shape of the relative enhancement of the f(R) matter power spectrum with respect to LCDM caused by the extra attractive gravitational force but fails to recover the correct amplitude. Introducing an effective linear power spectrum in the computation of the two-halo term to account for an underestimation of the chameleon suppression at intermediate scales in our approach, we accurately reproduce the measurements from the N-body simulations.
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 fields mass steeply increases with ambient density. Consequently, the chameleonic force is only sourced by a thin shell near the surface of dense objects, which significantly reduces its magnitude. In this paper, we argue that thin-shell conditions are equivalent to conducting boundary conditions in electrostatics. As an application, we use the analogue of the method of images to calculate the back-reaction (or self-force) of an object around a spherical gravitational source. Using this method, we can explicitly compute the violation of equivalence principle in the outskirts of galactic haloes (assuming an NFW dark matter profile): Intermediate mass satellites can be slower than their larger/smaller counterparts by as much as 10% close to a thin shell.
We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied $f(R)$ gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of $f(R)$ simulations. For example, a test simulation with $512^3$ particles in a box of size $512 , mathrm{Mpc}/h$ is now 5 times faster than before, while a Millennium-resolution simulation for $f(R)$ gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.
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