Loop contributions to the scalar power spectrum due to quartic order action in ultra slow roll inflation
arXiv (Cornell University)(2023)
摘要
[Abridged] In contemporary literature, the calculation of modifications to
the inflationary scalar power spectrum due to the loops from the higher order
interaction terms in the Hamiltonian have led to a discussion regarding the
validity of perturbation theory. Recently, there have been efforts to examine
the contributions to the scalar power spectrum due to the loops arising from
the cubic order terms in the action describing the perturbations, specifically
in inflationary scenarios that permit an epoch of ultra slow roll (USR). A
phase of USR inflation leads to significant observational consequences, such as
the copious production of primordial black holes. In this work, we study the
loop contributions to the scalar power spectrum in a scenario of USR inflation
arising due to the quartic order terms in the action describing the scalar
perturbations. We compute the loop contributions to the scalar power spectrum
due to the dominant term in the action at the quartic order. We consider a
scenario wherein a phase of USR is sandwiched between two stages of slow roll
inflation and analyze the behavior of the loop contributions in terms of the
parameters involved. We examine the late, intermediate and early epochs of USR
during inflation. In the inflationary scenario involving a late phase of USR,
for reasonable choices of the parameters, we show that the loop corrections are
negligible for the entire range of wave numbers. In the intermediate case, the
contributions from the loops prove to be scale invariant over large scales, and
we find that these contributions can amount to 30
spectrum. In the case wherein USR sets in early, we find that the loop
contributions could be negative and can dominate the power spectrum at the
leading order, which indicates a breakdown of the perturbative expansion. We
conclude with a brief summary and outlook.
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关键词
scalar power spectrum,inflation,loop contributions,quartic order
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