  We explore the possibility of the spontaneous symmetry breaking in 5D
conformally invariant gravity, whose action consists of a scalar field
nonminimally coupled to the curvature with its potential. Performing
dimensional reduction via ADM decomposition, we find that the model allows an
exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal
invariance with Gaussian warp factor, we show that it also admits a solution
which implement the spontaneous breaking of conformal symmetry. We investigate
its stability by performing the tensor perturbation and find the resulting
system is described by the conformal quantum mechanics. Possible applications
to the spontaneous symmetry breaking of time-translational symmetry along the
dynamical fifth direction and the brane-world scenario are discussed.
