  We are dealing with the validity of a large deviation principle for a class
of reaction-diffusion equations with polynomial nonlinearity, perturbed by a
Gaussian random forcing. We are here interested in the regime where both the
strength of the noise and its correlation are vanishing, on a length scale
$\epsilon$ and $\delta(\epsilon)$, respectively, with
$0<\epsilon,\delta(\epsilon)<<1$. We prove that, under the assumption that
$\epsilon$ and $\delta(\epsilon)$ satisfy a suitable scaling limit, a large
deviation principle holds in the space of continuous trajectories with values
both in the space of square-integrable functions and in Sobolev spaces of
negative exponent. Our result is valid, without any restriction on the degree
of the polynomial nor on the space dimension.
