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.
