  We investigate spontaneous symmetry breaking in a conformally invariant
gravitational model. In particular, we use a conformally invariant scalar
tensor theory as the vacuum sector of a gravitational model to examine the idea
that gravitational coupling may be the result of a spontaneous symmetry
breaking. In this model matter is taken to be coupled with a metric which is
different but conformally related to the metric appearing explicitly in the
vacuum sector. We show that after the spontaneous symmetry breaking the
resulting theory is consistent with Mach's principle in the sense that inertial
masses of particles have variable configurations in a cosmological context.
Moreover, our analysis allows to construct a mechanism in which the resulting
large vacuum energy density relaxes during evolution of the universe.
