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Published July 15, 2020 | Published + Submitted
Journal Article Open

Robust numerical computation of the 3D scalar potential field of the cubic Galileon gravity model at solar system scales


Direct detection of dark energy or modified gravity may finally be within reach due to ultrasensitive instrumentation such as atom interferometry capable of detecting incredibly small scale accelerations. Forecasts, constraints and measurement bounds can now too perhaps be estimated from accurate numerical simulations of the fifth force and its Laplacian field at solar system scales. The cubic Galileon gravity scalar field model (CGG), which derives from the DGP braneworld model, describes modified gravity incorporating a Vainshtein screening mechanism. The nonlinear derivative interactions in the CGG equation suppress the field near regions of high density, thereby restoring general relativity (GR) while far from such regions, field enhancement is comparable to GR and the equation is dominated by a linear term. This feature of the governing PDE poses some numerical challenges for computation of the scalar potential, force and Laplacian fields even under stationary conditions. Here we present a numerical method based on finite differences for solution of the static CGG scalar field for a 2D axisymmetric Sun-Earth system and a 3D Cartesian Sun-Earth-Moon system. The method relies on gradient descent of an integrated residual based on the normal attractive branch of the CGG equation. The algorithm is shown to be stable, accurate and rapidly convergent toward the global minimum state. We hope this numerical study, which can easily be extended to include smaller bodies such as detection satellites, will prove useful to future measurement of modified gravity force fields at solar system scales.

Additional Information

© 2020 American Physical Society. Received 24 February 2020; accepted 20 May 2020; published 9 July 2020. N. C. W. gratefully acknowledges financial support from a 2017 NASA Space Technology Research Fellowship (80NSSC17K0139). This research was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology (Caltech), under a contract with the National Aeronautics and Space Administration (80NM0018D0004). S. M. T. and N. C. W. wish to thank Dr. Peter Thompson for his efforts in designing and implementing the computing cluster used for the simulations. Jérôme Gleyzes, Jason Rhodes, Olivier Doré, Eric Huff, and Kristofer Pardo are also acknowledged for valuable discussions of dark energy and modified gravity.

Attached Files

Published - PhysRevD.102.024033.pdf

Submitted - 2003.02648.pdf


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