The Shape Dependence of Chameleon Gravity
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 observa...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2023
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| Online Access: | https://eprints.nottingham.ac.uk/76774/ |
| _version_ | 1848800936822046720 |
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| author | Briddon, Chad |
| author_facet | Briddon, Chad |
| author_sort | Briddon, Chad |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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 I introduce the software package SELCIE (\url{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. I compare the results produced by SELCIE with analytic results from the literature including discrete and continuous density distributions. I find strong (sub-percentage) agreement between the solutions calculated by SELCIE and the analytic solutions.
One consequence of this screening mechanism is that the force induced by the field is dependent on the shape of the source mass (a property that distinguishes it from gravity). Therefore an optimal shape must exist for which the chameleon force is maximised. Such a shape would allow experiments to improve their sensitivity by simply changing the shape of the source mass. In this work I use a combination of genetic algorithms and SELCIE to find shapes that optimise the force at a single point in an idealised experimental environment. I note that the method I use is easily customised, and so can be used to optimise a more realistic experiment involving particle trajectories or the force acting on an extended body. I find the shapes outputted by the genetic algorithm possess common characteristics, such as a preference for smaller source masses, and that the largest fifth forces are produced by small `umbrella'-like shapes with a thickness such that the source is unscreened but the field reaches its minimum inside the source. This remains the optimal shape even as we change the chameleon potential, and the distance from the source, and across a wide range of chameleon parameters. I find that by optimising the shape in this way the fifth force can be increased by $2.45$ times when compared to a sphere, centred at the origin, of the same volume and mass. |
| first_indexed | 2025-11-14T20:59:29Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-76774 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:59:29Z |
| publishDate | 2023 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-767742024-01-31T15:32:54Z https://eprints.nottingham.ac.uk/76774/ The Shape Dependence of Chameleon Gravity Briddon, Chad 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 I introduce the software package SELCIE (\url{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. I compare the results produced by SELCIE with analytic results from the literature including discrete and continuous density distributions. I find strong (sub-percentage) agreement between the solutions calculated by SELCIE and the analytic solutions. One consequence of this screening mechanism is that the force induced by the field is dependent on the shape of the source mass (a property that distinguishes it from gravity). Therefore an optimal shape must exist for which the chameleon force is maximised. Such a shape would allow experiments to improve their sensitivity by simply changing the shape of the source mass. In this work I use a combination of genetic algorithms and SELCIE to find shapes that optimise the force at a single point in an idealised experimental environment. I note that the method I use is easily customised, and so can be used to optimise a more realistic experiment involving particle trajectories or the force acting on an extended body. I find the shapes outputted by the genetic algorithm possess common characteristics, such as a preference for smaller source masses, and that the largest fifth forces are produced by small `umbrella'-like shapes with a thickness such that the source is unscreened but the field reaches its minimum inside the source. This remains the optimal shape even as we change the chameleon potential, and the distance from the source, and across a wide range of chameleon parameters. I find that by optimising the shape in this way the fifth force can be increased by $2.45$ times when compared to a sphere, centred at the origin, of the same volume and mass. 2023-12-12 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/76774/1/University_of_Nottingham_PhD_Thesis.pdf Briddon, Chad (2023) The Shape Dependence of Chameleon Gravity. PhD thesis, University of Nottingham. Modified Gravity Scalar-Tensor Screening Machine Learning Scalar field model |
| spellingShingle | Modified Gravity Scalar-Tensor Screening Machine Learning Scalar field model Briddon, Chad The Shape Dependence of Chameleon Gravity |
| title | The Shape Dependence of Chameleon Gravity |
| title_full | The Shape Dependence of Chameleon Gravity |
| title_fullStr | The Shape Dependence of Chameleon Gravity |
| title_full_unstemmed | The Shape Dependence of Chameleon Gravity |
| title_short | The Shape Dependence of Chameleon Gravity |
| title_sort | shape dependence of chameleon gravity |
| topic | Modified Gravity Scalar-Tensor Screening Machine Learning Scalar field model |
| url | https://eprints.nottingham.ac.uk/76774/ |