  We consider the Cahn-Hilliard equation in one space dimension, perturbed by
the derivative of a space and time white noise of intensity $\epsilon^{\frac
12}$, and we investigate the effect of the noise, as $\epsilon \to 0$, on the
solutions when the initial condition is a front that separates the two stable
phases. We prove that, given $\gamma< \frac 23$, with probability going to one
as $\epsilon \to 0$, the solution remains close to a front for times of the
order of $\epsilon^{-\gamma}$, and we study the fluctuations of the front in
this time scaling. They are given by a one dimensional continuous process, self
similar of order $\frac 14$ and non Markovian, related to a fractional Brownian
motion and for which a couple of representations are given.
