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

TL;DR

This paper develops a nonperturbative approach to study quantum fluctuation effects during a specific inflationary scenario, revealing how ultra-slow-roll inflation can amplify curvature perturbations despite cosmic friction.

Contribution

It introduces a Hartree-based nonperturbative method to analyze quantum effects in inflation, highlighting the impact of USR phases on curvature perturbations.

Findings

USR inflation causes significant growth in quantum fluctuation effects.

Cosmic friction can suppress the boost of curvature perturbations.

Two models illustrate the competition between growth and suppression.

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 $\Delta_B$ term. We consider the Universe undergoing the slow roll (SR)-ultra slow roll (USR) -slow roll (SR) inflation where in particular the presence of the USR inflation triggers the huge growth of $\Delta_B$ that in turn gives the boost effects to the curvature perturbations for the modes that leave horizon in the early times of the inflation. However, the cosmic friction term in the mode equation given by the Hubble parameter presumably prohibits the boost effects. Here we propose two representative models to illustrate these two competing terms.