  We consider the dynamics of a quantum scalar field in the background of a
slow-roll inflating Universe. We compute the one-loop quantum corrections to
the field and Friedmann equation of motion, in both a 1PI and a 2PI expansion,
to leading order in slow-roll. Generalizing the works of [1-3], we then solve
these equations to compute the effect on the primordial power spectrum, for the
case of a self-interacting inflaton and a self-interacting spectator field. We
find that for the inflaton the corrections are negligible due to the smallness
of the coupling constant despite the large IR enhancement of the loop
contributions. For a curvaton scenario, on the other hand, we find tension in
using the 1PI loop corrections, which may indicate that the quantum corrections
could be non-perturbatively large in this case, thus requiring resummation.
