The Classical Symmetron Force in Casimir Experiments

TL;DR

This paper calculates the symmetron force in laboratory-like plate-sphere setups, providing a way to use Casimir experiments to constrain symmetron parameters and test screened modified gravity theories.

Contribution

It introduces semi-analytical and numerical methods to compute symmetron forces in different regimes, linking theoretical models with experimental constraints.

Findings

Large spheres analyzed via proximity force approximation.

Small spheres treated as screened test particles.

Forecasts show future Casimir experiments can tightly constrain symmetron parameters.

Abstract

The symmetron is a typical example of screened modified gravity, wherein the symmetron force is dynamically suppressed in dense environments. This allows it to hide in traditional tests of gravity. However, the past decade has seen great experimental progress towards measuring screened forces in the laboratory or in space. Screening relies on nonlinearities in the equation of motion, which significantly complicates the theoretical analysis of such forces. Here, we present a calculation of the symmetron force between a dense plate and sphere surrounded by vacuum. This is done via semi-analytical approaches in two limiting cases, based on the size of the sphere: large spheres are analyzed via the proximity force approximation, whilst small spheres are treated as screened test particles. In the intermediate regime we solve the problem numerically. Our results allow us to make contact with Casimir force experiments, which often employ a plate and sphere configuration for practical reasons, and may therefore be used to constrain symmetrons. We use our results to forecast constraints on the symmetron's parameters for a hypothetical Casimir experiment that is based on the current state of the art. The forecasts compare favorably to other leading laboratory tests of gravity, particularly atom interferometry and bouncing neutrons. We thus conclude that near-future Casimir experiments will be capable of placing tight new bounds on symmetrons. Our results for the symmetron force are derived in a scale-invariant way, such that although we here focus on Casimir experiments, they may be applied to any other plate-sphere system, ranging from microscopic to astrophysical scales.