Non-perturbative wavefunction of the universe in inflation with (resonant) features

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction Psi[zeta(x)] non-perturbatively in zeta, but at first order in the amplitude of the oscillations. The expression of the wavefunction of the universe (WFU) is explicit and does not require solving partial differential equations. One finds qualitative deviations from perturbation theory for |zeta| greater than or similar to alpha(-2), where alpha >> 1 is the number of oscillations per Hubble time. Notably, the WFU exhibits distinct behaviours for negative and positive values of zeta (troughs and peaks respectively). While corrections for zeta < 0 remain relatively small, of the order of the oscillation amplitude, positive zeta yields substantial effects, growing exponentially as e(pi alpha/2) in the limit of large zeta. This indicates that even minute oscillations give large effects on the tail of the distribution.