Classical symmetron force in Casimir experiments

Physical review. D/Physical review. D., vol. 101

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 toward 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 semianalytical 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.

Authors 6

1. Benjamin Elder

   University of Nottingham

   Affiliation as printed

   School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom

2. Valeri Vardanyan Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Kavli Institute for the Physics and Mathematics of the Universe · Leiden Observatory · The University of Tokyo

   Affiliation as printed

   Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Chiba 277-8583, Japan

   Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, Netherlands

   Lorentz Institute for Theoretical Physics, Leiden University, P.O. Box 9506, 2300 RA Leiden, Netherlands

3. Y. Akrami

   Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Observatoire de Paris · École Normale Supérieure - PSL · Sorbonne Université · Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères · Laboratoire de Physique de l'Ecole Normale Supérieure

   Affiliation as printed

   Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France

   Observatoire de Paris, Université PSL, Sorbonne Université, LERMA, 75014 Paris, France

   Astrophysique (24 rue Lhomond 75005 Paris - France)

   LERMA (UMR_8112) - Laboratoire d'Etude du Rayonnement et de la Matière en Astrophysique (61, avenue de l'Observatoire - 75014 PARIS - France)

4. Philippe Brax

   Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · CEA Paris-Saclay - Etablissement de Saclay · Institut de Physique Théorique

   Affiliation as printed

   Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif/Yvette Cedex, France

   IPHT - Institut de Physique Théorique - UMR CNRS 3681 (Institut de Physique Théorique Orme des Merisiers batiment 774 Point courrier 136 CEA/DSM/IPhT CEA/Saclay F-91191 Gif-sur-Yvette Cedex - France)

5. Anne-Christine Davis

   University of Cambridge

   Affiliation as printed

   DAMTP, Centre for Mathematical Sciences, University of Cambridge, CB3 0WA, United Kingdom

6. R. S. Decca

   Indiana University Indianapolis · Indiana University – Purdue University Indianapolis

   Affiliation as printed

   Department of Physics, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Bldg LD154, Indianapolis, Indiana 46202, USA