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One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes
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One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes
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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 $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ 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.
Forward citations
Cited by 4 Pith papers
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Derives all-order Hamiltonians via EFT of inflation for USR models and shows L-loop corrections to CMB-scale perturbations scale as (ΔN P_e L)^L, exiting perturbative control at L=4 for typical ΔN≈2.5.
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Non-Perturbative Hamiltonian and Higher Loop Corrections in USR Inflation
In USR inflation with an idealized instantaneous sharp transition to slow-roll, higher loop corrections to curvature perturbations on CMB scales grow rapidly with loop order L and may exit perturbative control.
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