Geophysical constraint on a relic background of the dilatons

According to a scenario in string cosmology, a relic background of light dilatons can be a significant component of the dark matter in the Universe. A new approach of searching for such a dilatonic background by observing Earth's surface gravity was proposed in my previous work. In this paper, the concept of the geophysical search is briefly reviewed, and the geophysical constraint on the dilaton background is presented as a function of the strength of the dilaton coupling, $q_b^2$. For simplicity, I focus on massless dilatons and assume a simple Earth model. With the current upper limit on $q_b^2$, we obtain the upper limit on the dimensionless energy density of the massless background, $\Omega_{DW}h^2_{100} \leq 6 \times 10^{-7}$, which is about one-order of magnitude more stringent than the one from astrophysical observations, at the frequency of $\sim$ 7 $\times$ 10$^{-5}$ Hz. If the magnitude of $q_b^2$ is experimentally found to be smaller than the current upper limit by one order of magnitude, the geophysical upper limit on $\Omega_{DW}h^2_{100}$ becomes less stringent and comparable to the one obtained from the astrophysical observations.