Consequences of a stochastic approach to the conformal invariance of
  inflationary correlators
  We provide a general formalism to calculate the infrared correlators of
multiple interacting scalar fields in the de Sitter space by means of the
stochastic approach. These scalar fields are treated as test fields and hence
our result is applicable to the models such as the curvaton scenario where the
fields that yield initially isocurvature modes do not contribute to the cosmic
energy density during inflationary expansion. The stochastic formalism combined
with the argument of conformal invariance of the correlators reflecting the de
Sitter isometries allows us to fix the form and amplitude of the three-point
functions completely and partially for the four-point functions in terms of
calculable quantities. It turns out that naive scaling argument employed in the
previous literature does not necessarily hold and we derive the necessary and
sufficient condition for the correlator to obey the naive scaling. We also find
that correlation functions can in principle exhibit more complicated structure
than argued in the literature.
