φenics: Vainshtein screening with the finite element method

Braden, Jonathan; Burrage, Clare; Elder, Benjamin; Saadeh, Daniela

Abstract

Within the landscape of modified theories of gravity, progress in understanding the behaviour of, and developing tests for, screening mechanisms has been hindered by the complexity of the field equations involved, which are nonlinear in nature and characterised by a large hierarchy of scales. This is especially true of Vainshtein screening, where the fifth force is suppressed by high-order derivative terms which dominate within a radius much larger than the size of the source, known as the Vainshtein radius. =-1 In this work, we present the numerical code φenics, building on the FEniCS library, to solve the full equations of motion from two theories of interest for screening: a model containing high-order derivative operators in the equation of motion and one characterised by nonlinear self-interactions in two coupled scalar fields. We also include functionalities that allow the computation of higher-order operators of the scalar fields in post-processing, enabling us to check that the profiles we find are consistent solutions within the effective field theory. These two examples illustrate the different challenges experienced when trying to simulate such theories numerically, and we show how these are addressed within this code. The examples in this paper assume spherical symmetry, but the techniques may be straightforwardly generalised to asymmetric configurations. This article therefore also provides a worked example of how the finite element method can be employed to solve the screened equations of motion. φenics is publicly available and can be adapted to solve other theories of screening.

Citation

Braden, J., Burrage, C., Elder, B., & Saadeh, D. (2021). φenics: Vainshtein screening with the finite element method. Journal of Cosmology and Astroparticle Physics, 2021(03), Article 010. https://doi.org/10.1088/1475-7516/2021/03/010

• Journal Article Type: Article
• Acceptance Date: Jan 12, 2021
• Online Publication Date: Mar 8, 2021
• Publication Date: Mar 8, 2021
• Deposit Date: May 17, 2021
• Publicly Available Date: Mar 9, 2022
• Journal: Journal of Cosmology and Astroparticle Physics
• Electronic ISSN: 1475-7516
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 2021
• Issue: 03
• Article Number: 010
• DOI: https://doi.org/10.1088/1475-7516/2021/03/010
• Keywords: Astronomy and Astrophysics
• Public URL: https://nottingham-repository.worktribe.com/output/5557471
• Publisher URL: https://iopscience.iop.org/article/10.1088/1475-7516/2021/03/010
• Additional Information: This is the Accepted Manuscript version of an article accepted for publication in Journal of Cosmology and Astroparticle Physics . IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://iopscience.iop.org/article/10.1088/1475-7516/2021/03/010