A Naturally Large Four-Point Function in Single Field Inflation
  Non-Gaussianities of the primordial density perturbations have emerged as a
very powerful possible signal to test the dynamics that drove the period of
inflation. While in general the most sensitive observable is the three-point
function in this paper we show that there are technically natural inflationary
models where the leading source of non-Gaussianity is the four-point function.
Using the recently developed Effective Field Theory of Inflation, we are able
to show that it is possible to impose an approximate parity symmetry and an
approximate continuos shift symmetry on the inflaton fluctuations that allow,
when the dispersion relation is of the form $\omega\sim c_s k$, for a unique
quartic operator, while approximately forbidding all the cubic ones. The
resulting shape for the four-point function is unique. In the models where the
dispersion relation is of the form $\omega\sim k^2/M$ a similar construction
can be carried out and additional shapes are possible.
