Beyond Perturbation Theory in Inflation [article]

Marco Celoria, Paolo Creminelli, Giovanni Tambalo, Vicharit Yingcharoenrat
2021 arXiv   pre-print
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
more » ... e-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^-1/4ζ^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.
arXiv:2103.09244v2 fatcat:nnlqjz2l2rbqjlfkqnrxza7esm