# New Bounds on Dark Energy Induced Fifth Forces

## TL;DR

This paper derives bounds on a scalar field associated with dark energy that could cause fifth forces, using experimental and observational data, and predicts a testable interaction range within current experimental reach.

## Contribution

It provides new theoretical bounds on the scalaron mass in scalar-tensor theories related to dark energy, connecting them with experimental constraints from gravity tests and cosmological observations.

## Key findings

- Scalar interaction range constrained to 4-68 micrometers.
- Strong bounds on scalaron mass from Eöt-Wash and cosmological data.
- Predicted interaction range is accessible to future experiments.

## Abstract

We consider the gravitational Wilsonian effective action at low energy when all the particles of the standard model have decoupled. When the ${\cal R}^2$ terms dominate, the theory is equivalent to a scalar-tensor theory with the universal coupling $\beta=1/\sqrt 6$ to matter for which we present strong lower and upper bounds on the scalaron mass $m$ obtained by using results from the E\"ot-Wash experiment on the modification of the inverse-square law, the observations of the hot gas of galaxy clusters and the Planck satellite data on the neutrino masses. In terms of the range of the scalar interaction mediated over a distance of order $m^{-1}$, this leads to the small interval $4\,\mu m \lesssim m^{-1} \lesssim 68\, \mu m$ within reach of future experimental tests of deviations from Newton's gravitational inverse-square law.