  We consider the approximation via modulation equations for nonlinear SPDEs on
unbounded domains with additive space time white noise. Close to a bifurcation
an infinite band of eigenvalues changes stability, and we study the impact of
small space-time white noise on this bifurcation.
  As a first example we study the stochastic Swift-Hohenberg equation on the
whole real line. Here due to the weak regularity of solutions the standard
methods for modulation equations fail, and we need to develop new tools to
treat the approximation.
  As an additional result we sketch the proof for local existence and
uniqueness of solutions for the stochastic Swift-Hohenberg and the complex
Ginzburg Landau equations on the whole real line in weighted spaces that allow
for unboundedness at infinity of solutions, which is natural for translation
invariant noise like space-time white noise. Moreover we use energy estimates
to show that solutions of the Ginzburg-Landau equation are H\"older continuous
and have moments in those functions spaces. This gives just enough regularity
to proceed with the error estimates of the approximation result.
