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Two-loop corrections in power spectrum in models of inflation with PBHs formation
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We calculate the two-loop corrections in primordial power spectrum in models of single field inflation incorporating an intermediate USR phase employed for PBHs formation. Among the total eleven one-particle irreducible Feynman diagrams, we calculate the corrections from the "double scoop" two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate that the fractional two-loop correction in power spectrum scales like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase.
Forward citations
Cited by 3 Pith papers
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Analytic asymptotics show the dip in the SR-USR-SR curvature power spectrum comes from cancellation between two growing modes, not a constant-versus-growing cancellation.
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One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production
For E-type alpha-attractor inflation models tuned to produce asteroid-mass primordial black holes, the one-loop correction from cubic interactions is only a few percent of the tree-level power spectrum.
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