Quintessence, the gravitational constant, and gravity

Dynamical vacuum energy or quintessence, a slowly varying and spatially inhomogeneous component of the energy density with negative pressure, is currently consistent with observational data. One potential difficulty with the idea of quintessence is that couplings to ordinary matter should be strongly suppressed so as not to lead to observable time variations of the constants of nature. We further explore the possibility of an explicit coupling between the quintessence field and the curvature. Since such a scalar field gives rise to another gravity force of long range $\left(\gtrsim H_0^{-1}\right),$ the solar system experiments put a constraint on the nonminimal coupling: $|\xi |\lesssim {10}^{-2}.$