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One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes
As one of the promising candidates of cold dark matter (DM), primordial black
holes (PBHs) were formed due to the collapse of over-densed regions generated
by the enhanced curvature perturbations during the radiation-dominated era. The
enhanced curvature perturbations are expected to be non-Gaussian in some
relevant inflation models and hence the higher-order loop corrections to the
curvature power spectrum might be non-negligible as well as altering the
abundance of PBHs. In this paper, we calculate the one-loop correction to the
curvature power spectrum with local-type non-Gaussianities characterizing by
and standing for the quadratic and cubic
non-Gaussian parameters, respectively. Requiring that the one-loop correction
be subdominant, we find a perturbativity condition, namely
, where is a constant
coefficient which can be explicitly calculated in the given model and
denotes the variance of Gaussian part of enhanced curvature perturbation, and
such a perturbativity condition can provide a stringent constraint on the
relevant inflation models for the formation of PBHs.Comment: 6 pages, 5 figure
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