Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll
  Inflation
  We calculate the four point correlation function for scalar perturbations in
the canonical model of slow-roll inflation. We work in the leading slow-roll
approximation where the calculation can be done in de Sitter space. Our
calculation uses techniques drawn from the AdS/CFT correspondence to find the
wave function at late times and then calculate the four point function from it.
The answer we get agrees with an earlier result in the literature, obtained
using different methods. Our analysis reveals a subtlety with regard to the
Ward identities for conformal invariance, which arises in de Sitter space and
has no analogue in AdS space. This subtlety arises because in de Sitter space
the metric at late times is a genuine degree of freedom, and hence to calculate
correlation functions from the wave function of the Universe at late times, one
must fix gauge completely. The resulting correlators are then invariant under a
conformal transformation accompanied by a compensating coordinate
transformation which restores the gauge.
