Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics II: Quartic interactions and consistency relations

Abstract

We prove explicitly the absence of one-loop corrections to large scales from small scales in transient non-slow-roll dynamics. Specifically, we address loop corrections to the primordial power spectrum, relative to tree-level, that are independent of the ratio between the two scales. We review all the necessary components, adapted to our context, to express one-loop diagrams as three-point functions, emphasizing the crucial role played by quartic interactions. Notably, we include the quartic Hamiltonian induced by the cubic Lagrangian and quartic interactions that are ensured by diffeomorphism invariance. We then explicitly prove consistency relations for an arbitrary transient non-slow-roll phase involving operators with (time) derivatives. Finally, we calculate one-loop corrections by including contributions from the relevant cubic and quartic interactions, and express the final result as a total derivative term over comoving momenta, utilizing the consistency relations we established. This leads us to conclude that one-loop corrections to long-wavelength modes are unaffected by the physics of short and enhanced modes in non-slow-roll dynamics.

48 pages. v2: Corrected a few typos, reference added and expanded the discussion on Mode functions and Hankel functions relations in Sec. 6.1. Version published in JHEP

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Cited by in corpus (12)

• Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics
• Gravitational waves in ultra-slow-roll and their anisotropy at two loops
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop
• Incorporating Backreaction in One-Loop Corrections in Ultra-Slow-Roll Inflation
• Ultra-Slow-Roll Inflation on the Lattice II: Nonperturbative Curvature Perturbation
• One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production
• Dip and non-linearity in the curvature perturbation from inflation with a transient non-slow-roll stage
• Loops in inflation with strongly non-geodesic motion
• Stochastic Inflation with Interacting Noises
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Separate universe in multifield inflation: a phase-space approach