# Constraining a nonminimally coupled curvature-matter gravity model with ocean experiments

## TL;DR

This paper uses ocean experiments to set bounds on a nonminimally coupled gravity model, constraining the Yukawa potential's strength and range based on deviations from Newtonian gravity observed in seawater.

## Contribution

It provides new bounds on the Yukawa potential parameters in a non-minimally coupled gravity theory using ocean-based experimental data.

## Key findings

- Upper bound on the Yukawa range: 57.4 km
- Constraint on the Yukawa strength: α < 0.002
- Extra force affects hydrostatic equilibrium in seawater

## Abstract

We examine the constraints on the Yukawa regime from the non-minimally coupled curvature-matter gravity theory arising from deep underwater ocean experiments. We consider the geophysical experiment of Zumberge et al. of 1991 for searching deviations of Newton's inverse square law in ocean. In the context of non-minimally coupled curvature-matter theory of gravity the results of Zumberge et al. can be used to obtain an upper bound both on the strength $\alpha$ and range $\lambda$ of the Yukawa potential arising from the non-relativistic limit of the non-minimally coupled theory. The existence of an upper bound on $\lambda$ is related to the presence of an extra force, specific of the nonminimally coupled theory, which depends on $\lambda$ and on the gradient of mass density, and has an effect in the ocean because of compressibility of seawater. These results can be achieved after a suitable treatment of the conversion of pressure to depth in the ocean by resorting to the equation of state of seawater and taking into account the effect of the extra force on hydrostatic equilibrium. If the sole Yukawa interaction were present the experiment would yield only a bound on $\alpha$, while, in the presence of the extra force we find an upper bound on the range: $\lambda_{\rm max}= 57.4$ km. In the interval $1 \,{\rm m}<\lambda<\lambda_{\rm max}$ the upper bound on $\alpha$ is consistent with the constraint $\alpha<0.002$ found in Zumberge et al.