Influence functionals, decoherence and conformally coupled scalars

C Burrage,C Käding,J Minář,P Millington

doi:10.1088/1742-6596/1275/1/012041

Abstract

Some of the simplest modifications to general relativity involve the coupling of additional scalar fields to the scalar curvature. By making a Weyl rescaling of the metric, these theories can be mapped to Einstein gravity with the additional scalar fields instead being coupled universally to matter. The resulting couplings to matter give rise to scalar fifth forces, which can evade the stringent constraints from local tests of gravity by means of so-called screening mechanisms. In this talk, we derive evolution equations for the matrix elements of the reduced density operator of a toy matter sector by means of the Feynman-Vernon influence functional. In particular, we employ a novel approach akin to the LSZ reduction more familiar to scattering-matrix theory. The resulting equations allow the analysis, for instance, of decoherence induced in atom-interferometry experiments by these classes of modified theories of gravity.

Highlights

There are many pointers to a need to extend the Standard Model of particle physics (SM) and/or general relativity, not least the dark matter and dark energy problems, and the simplest extensions often involve additional scalar fields
Some of the simplest modifications to general relativity involve the coupling of additional scalar fields to the scalar curvature
If the scalar fields are heavy on astrophysical scales and stable on cosmological time-scales, they may compose the relic density of dark matter, produced thermally in the early universe

Summary

Introduction

There are many pointers to a need to extend the Standard Model of particle physics (SM) and/or general relativity, not least the dark matter and dark energy problems, and the simplest extensions often involve additional scalar fields. If these new fields are neutral under the SM gauge groups, they may couple to the SM via the Higgs portal or through a non-minimal coupling to the Ricci scalar (of Brans-Dicke type [1]), mediating interactions with hidden sectors. Working to leading order in the expansion of the coupling function, and in a constant density environment, the chameleon field acquires a background value of. Working with operators up to dimension four only, the action for the ‘atom’ field φ and the chameleon fluctuations χ can be separated into free and (self-)interacting parts as

M 2χ2 2

Epφ sin p0