  In this paper we establish lower and upper Gaussian bounds for the solutions
to the heat and wave equations driven by an additive Gaussian noise, using the
techniques of Malliavin calculus and recent density estimates obtained by
Nourdin and Viens. In particular, we deal with the one-dimensional stochastic
heat equation in $[0,1]$ driven by the space-time white noise, and the
stochastic heat and wave equations in $\mathbb{R}^d$ ($d\geq 1$ and $d\leq 3$,
respectively) driven by a Gaussian noise which is white in time and has a
general spatially homogeneous correlation.
