Numerical 1-loop correction from a potential yielding ultra-slow-roll dynamics

Abstract

Single-field models of inflation might lead to amplified scalar fluctuations on small scales due, for example, to a transient ultra-slow-roll phase. It was argued by Kristiano $\&$ Yokoyama in arXiv:2211.03395 that the enhanced amplitude of the scalar power spectrum on small scales has the potential to induce a sizeable 1-loop correction to the spectrum at large scales. In this work, we repeat the calculation for the 1-loop correction presented in arXiv:2211.03395. We closely follow their assumptions but evaluate the loop numerically. This allows us to consider both instantaneous and smooth transitions between the slow-roll and ultra-slow-roll phases. In particular, we generate models featuring realistic, smooth evolution from an analytic inflationary potential. We find that, upon fixing the amplitude of the peak in the power spectrum at short scales, the resulting 1-loop correction is not significantly reduced by considering a smooth evolution. In particular, for a power spectrum with a tree-level peak amplitude potentially relevant for small-scale phenomenology, e.g. primordial black hole production, the 1-loop correction on large scales is a few percent of the tree-level power spectrum.

32 pages, 8 figures, accepted for publication in JCAP

References in corpus (10)

• Primordial Black Holes as Dark Matter
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Primordial black hole dark matter from single field inflation
• Primordial Black Holes and Slow-Roll Violation
• Ultra slow-roll inflation demystified
• The "in-in" Formalism and Cosmological Perturbations
• A note on the role of the boundary terms for the non-Gaussianity in general k-inflation
• The Primordial Black Hole Formation from Single-Field Inflation is Still Not Ruled Out

Cited by in corpus (23)

• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Ultra-Slow-Roll Inflation on the Lattice I: Backreaction and Nonlinear Effects
• No time to derive: unraveling total time derivatives in in-in perturbation theory
• Large fluctuations and Primordial Black Holes
• 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
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Quantum loop corrections in the modified gravity model of Starobinsky inflation with primordial black hole production
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Conservation of superhorizon curvature perturbations at one loop: Backreaction in the in-in formalism and Renormalization
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Incorporating Backreaction in One-Loop Corrections in Ultra-Slow-Roll Inflation
• Role of the counterterms in the conservation of superhorizon curvature perturbations at one loop
• 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
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Non-Gaussianities and Primordial Black Holes
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Stochastic Inflation with Interacting Noises
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function