Power spectrum of primordial perturbations during ultra-slow-roll inflation with back reaction effects

Abstract

We develop a nonperturbative method through the Hartree factorization to examine the quantum fluctuation effects on the single-field inflationary models in a spatially flat FRW cosmological space-time. Apart from the background field equation as well as the Friedmann equation with the corrections of quantum field fluctuations, the modified Mukhanov-Sasaki equations for the mode functions of the quantum scalar field are also derived by introducing the nonzero ∆ B term. We

Amplification of primordial perturbations from the rise or fall of the inflaton

“…First, we should keep in mind that, even if |A n | becomes closer to unity during the USR period with other parameters, the strong coupling of perturbations does not prevent the non-adiabatic particle production because it completes before the USR period, which amplifies the curvature perturbations mainly on superhorizon scales where gravitational interactions rather than scalar field interactions dominate. In that case, although the precise calculation of the power spectrum requires more careful methods, such as the stochastic formalism [107][108][109][110][111][112] and the Hartree factorization [113], the perturbation enhancement definitely occurs because the particle production itself can be described with the linear perturbation theory. Second, strictly speaking, we need to check the infinite number of the higher order contributions, A n even for n > 6, but, in our model, the smoothing out is done with the tanh function (see section 5.1) and therefore we can expect the similar behavior even for n > 6.…”