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

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.