Primordial power spectrum features and consequences
  The present Cosmic Microwave Background (CMB) temperature and polarization
anisotropy data is consistent with not only a power law scalar primordial power
spectrum (PPS) with a small running but also with the scalar PPS having very
sharp features. This has motivated inflationary models with such sharp
features. Recently, even the possibility of having nulls in the power spectrum
(at certain scales) has been considered. The existence of these nulls has been
shown in linear perturbation theory. What shall be the effect of higher order
corrections on such nulls? Inspired by this question, we attempt to calculate
quantum radiative corrections to the Fourier transform of the two-point
function in a toy field theory and address the issue of how these corrections
to the power spectrum behave in models in which the tree-level power spectrum
has a sharp dip (but not a null). In particular, we consider the possibility of
the relative enhancement of radiative corrections in a model in which the
tree-level spectrum goes through a dip in power at a certain scale. The mode
functions of the field (whose power spectrum is to be evaluated) are chosen
such that they undergo the kind of dynamics that leads to a sharp dip in the
tree level power spectrum. Next we consider the situation in which this field
has quartic self interactions and find one loop correction in a suitably chosen
renormalization scheme. We thus attempt to answer the following key question in
the context of this toy model (which is as important in the realistic case): in
the chosen renormalization scheme, can quantum radiative corrections get
enhanced relative to tree-level power spectrum at scales at which sharp dips
appear in the tree-level spectrum?
