Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization

Abstract

We show that the superhorizon-limit curvature perturbations are conserved at one-loop level in single-field inflation models with a transient non-slow-roll period. We take the spatially-flat gauge, where the backreaction plays a crucial role for the conservation of superhorizon curvature perturbations unless the counter terms are tuned. We calculate the backreaction with the in-in formalism. In addition, we explicitly show the renormalization of the UV divergences with the counter terms.

25 pages, 2 figures, v3: minor revision, published version + Appendix B

References in corpus (28)

• Primordial Black Holes as Dark Matter
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Conformal Symmetries of Adiabatic Modes in Cosmology
• Questions on calculation of primordial power spectrum with large spikes: the resonance model case
• Primordial Black Holes
• Constraining Primordial Black Hole Formation from Single-Field Inflation
• A note on the role of the boundary terms for the non-Gaussianity in general k-inflation
• No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
• Amplification of Primordial Perturbations from the Rise or Fall of the Inflaton
• Power spectrum of primordial perturbations during ultra-slow-roll inflation with back reaction effects
• Squeezed bispectrum and one-loop corrections in transient constant-roll inflation
• Primordial Black Holes Arise When The Inflaton Falls
• Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism
• Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation
• One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
• Inflationary Butterfly Effect: Non-perturbative Dynamics From Small-Scale Features
• Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects
• Cancellation of quantum corrections on the soft curvature perturbations
• Numerical 1-loop correction from a potential yielding ultra-slow-roll dynamics
• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• Loop contributions to the scalar power spectrum due to quartic order action in ultra slow roll inflation
• One-loop infrared rescattering by enhanced scalar fluctuations during inflation
• Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics II: Quartic interactions and consistency relations
• Comparing sharp and smooth transitions of the second slow-roll parameter in single-field inflation
• Proving the absence of large one-loop corrections to the power spectrum of curvature perturbations in transient ultra-slow-roll inflation within the path-integral approach
• Roles of boundary and equation-of-motion terms in cosmological correlation functions
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• One-loop corrections to the E-type $\alpha$-attractor models of inflation and primordial black hole production

Cited by in corpus (5)

• 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
• Stochastic Inflation with Interacting Noises
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function