Obtaining a scalar fifth force for matter via a conformal coupling to the scalar field

TL;DR

This paper proposes a conformal coupling of matter to a scalar field within special relativity, leading to a potentially large scalar fifth force that is suppressed at large densities, consistent with current observations.

Contribution

It introduces a conformal coupling framework for matter and scalar fields that allows a strong fifth force while respecting observational constraints.

Findings

Scalar fifth force strength can reach the order of $1/\Lambda_E^2$.

Interaction range decreases with ambient density, staying below 80 micrometers.

The framework preserves general relativity even with scalar interactions.

Abstract

In the framework of special relativity (SR), I propose that matter conformally couples to a scalar field through the Lagrangian density of matter, whether matter is characterized by classical or by quantum (statistical) mechanics. The largest interaction strength of the scalar-mediated force can achieve the order of $1/\Lambda_E^2$ with the cosmological constant $\Lambda_E\approx 2.4\,\rm{meV}$. This is about 60 orders of magnitude larger than Newtonian gravity, i.e., ${(M_{\mathrm{Pl}}/\Lambda_E)}^2\sim 10^{60}$, where $M_{\mathrm{Pl}}\approx2.4\times 10^{18}\, \rm{GeV} $ is the reduced Planck energy. However, the discrete $\mathbb{Z}_2$ symmetry of the conformal coupling does not allow a massless scalar field, satisfying the constraint that no evidence of the long range force is observed. The interaction range of the force is inversely proportional to the square root of the ambient density. Therefore, in the general situation in which the ambient density is larger than the current cosmic density, the interaction range is always smaller than $1/\Lambda_E \approx 80\, \mu\rm{m}$. The form of general relativity (GR) still holds even when the energy-momentum tensors of the quintessence and the conformal interaction are included. The main purpose here is to overcome the puzzle in \cite{hcz2}, i.e., which frame is physical.