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φenics: Vainshtein screening with the finite element method

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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.

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.
Original languageEnglish
Article number010
Number of pages48
JournalJournal of Cosmology and Astroparticle Physics
Issue numberMarch 2021
Publication statusPublished - 8 Mar 2021


  • 2011.07037v2

    Rights statement: This Accepted Manuscript is available for reuse under a CC BY-NC-ND licence after the 12 month embargo period provided that all the terms and conditions of the licence are adhered to. © 2021 IOP Publishing Ltd and Sissa Medialab.

    Accepted author manuscript (Post-print), 1.33 MB, PDF document

    Due to publisher’s copyright restrictions, this document is not freely available to download from this website until: 8/03/22

    Licence: CC BY-NC-ND

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