  We consider the impact of additive Gaussian white noise on a supercritical
pitchfork bifurcation in an unbounded domain. As an example we focus on the
stochastic Swift-Hohenberg equation with polynomial nonlinearity. Here we
identify the order where small noise first impacts the bifurcation. Using an
approximation via modulation equations, we provide a tool to analyse how the
noise influences the dynamics close to a change of stability.
