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Two-loop corrections in power spectrum in models of inflation with PBHs formation
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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 5 Pith papers
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Scale-Dependent Loop Corrections to the Inflationary Power Spectrum
One-loop gravitational corrections in inflationary models with scale-dependent features are renormalizable and vanish on large and small scales, preserving perturbativity of CMB-fit feature models.
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Stochastic Inflation with Interacting Noises
The stochastic noise amplitude is modified to (H/2π) * sqrt(1 + ΔP_R / P0_R) to account for one-loop corrections in interacting theories, demonstrated in a three-phase SR-USR-SR setup for PBH formation.
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Hamiltonians to all Orders in Perturbation Theory and Higher Loop Corrections in Single Field Inflation with PBHs Formation
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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Evolution of Linear Perturbations under Time-Dependent Hubble Friction I: SR-USR-SR Inflation
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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