Beyond perturbation theory in inflation

Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime non-Gaussianities are important and perturbation theory breaks down for vertical bar zeta vertical bar >= vertical bar f(NL vertical bar)(-1). In this paper we show that this regime is amenable to a semiclassical treatment, h -> 0. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction proportional to lambda zeta(4). Numerical and analytical methods show that the tail of the probability distribution of zeta goes as exp(- lambda(-1/4) zeta(3/2)), with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes.

Automated summary

This paper demonstrates that non-perturbative effects of non-Gaussian perturbations in inflationary cosmology can be addressed through a semiclassical treatment. Numerical and analytical methods reveal a clear non-perturbative dependence in the tail of the probability distribution.