Numerical Methods for Scalar Field Dark Energy in Table-top Experiments and Lunar Laser Ranging

• DOI: 10.48550/arxiv.2401.16179
• Publication Date: 2024-01-29
• Authors: Hauke Fischer; René I. P. Sedmik
• Keywords: Ranging; Table (database)

Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating configurations within respective experiments. This paper focuses onto less-explored environment-dependent dilaton field, which emerges in strong coupling limit string theory. Due its exponential self-coupling, this can exhibit significantly steeper slopes compared and fields, equations motion be challenging solve with standard machine precision. We present first exact solution for geometry a vacuum region between two infinitely extended parallel plates. serves benchmark testing accuracy numerical solvers. By reparametrizing model transforming motion, we show how make computable across entire experimentally accessible parameter space. To simulate one- two-mirror geometries, well spherical configurations, introduce non-uniform finite difference method. Additionally, provide an algorithm solving stationary Schr\"odinger equation fermion one dimension presence field. The algorithms developed here are not limited but applied similar scalar-tensor theories well. demonstrate applications at hand Our computational tools practical variety experimental contexts, including gravity resonance spectroscopy (qBounce), Lunar Laser Ranging (LLR), upcoming Casimir Non-Newtonian Force Experiment (CANNEX). A Mathematica implementation all is provided.