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