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.

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.

We discuss the trapping of cold atoms within microscopic voids drilled perpendicularly through the axis of an optical waveguide. The dimensions of the voids considered are between 1 and 40 optical wavelengths. By simulating light transmission across the voids, we find that appropriate shaping of the voids can substantially reduce the associated loss of optical power. Our results demonstrate that the formation of an optical cavity around such a void could produce strong coupling between the atoms and the guided light. By bringing multiple atoms into a single void and exploiting collective enhancement, cooperativities ~400 or more should be achievable. The simulations are carried out using a finite difference time domain method. Methods for the production of such a void and the trapping of cold atoms within it are also discussed.

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 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 a φ /a Newt ≈ 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. We also discuss the optimal density profiles for detecting the fifth force in the upcoming observational surveys.

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.