Scalar correlation functions in de Sitter space from the stochastic
  spectral expansion
  We consider light scalar fields during inflation and show how the stochastic
spectral expansion method can be used to calculate two-point correlation
functions of an arbitrary local function of the field in de Sitter space. In
particular, we use this approach for a massive scalar field with quartic
self-interactions to calculate the fluctuation spectrum of the density contrast
and compare it to other approximations. We find that neither Gaussian nor
linear approximations accurately reproduce the power spectrum, and in fact
always overestimate it. For example, for a scalar field with only a quartic
term in the potential, $V=\lambda\phi^4/4$, we find a blue spectrum with
spectral index $n-1=0.579\sqrt{\lambda}$.
