Beyond perturbation theory in inflation
Marco Celoria, Paolo Creminelli, Giovanni Tambalo, Vicharit Yingcharoenrat
Abstract
Abstract 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 |ζ| ≳ | f NL | -1 . In this paper we show that this regime is amenable to a semiclassical treatment, ħ → 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 ∝λζ̇ 4 . Numerical and analytical methods show that the tail of the probability distribution of ζ goes as exp(-λ -1/4 ζ 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.