Inflation is always semi-classical: Diffusion domination overproduces Primordial Black Holes

Abstract

We use the Hamilton-Jacobi (H-J) formulation of stochastic inflation to describe the evolution of the inflaton during a period of Ultra-Slow Roll (USR), taking into account the field's velocity and its gravitational backreaction. We demonstrate how this formalism allows one to modify existing slow-roll (SR) formulae to be fully valid outside of the SR regime. We then compute the mass fraction, $\beta$, of Primordial Black Holes (PBHs) formed by a plateau in the inflationary potential. By fully accounting for the inflaton velocity as it enters the plateau, we find that PBHs are generically overproduced before the inflaton's velocity reaches zero, ruling out a period of free diffusion or even stochastic noise domination on the inflaton dynamics. We also examine a local inflection point and similarly conclude that PBHs are overproduced before entering a quantum diffusion dominated regime. We therefore surmise that the evolution of the inflaton is always predominantly classical with diffusion effects always subdominant. Both the plateau and the inflection point are characterized by a very sharp transition between the under- and over-production regimes. This can be seen either as severe fine-tunning on the inflationary production of PBHs, or as a very strong link between the fraction $\beta$ and the shape of the potential and the plateau's extent.

24 pages, 7 figures, 3 Appendices. Minor changes from v1, matches version accepted for publication in JCAP

References in corpus (12)

• Constraints on Primordial Black Holes
• Primordial Black Holes as a dark matter candidate
• The Threshold for Primordial Black Hole Formation: a Simple Analytic Prescription
• Gravitational waves from a universe filled with primordial black holes
• Ultra slow-roll inflation demystified
• On the divergences of inflationary superhorizon perturbations
• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• The Formation Probability of Primordial Black Holes
• Ultra-slow-roll inflation with quantum diffusion
• Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism
• Power spectrum in stochastic inflation
• Beyond Perturbation Theory in Inflation

Cited by in corpus (31)

• Inflation and Primordial Black Holes
• Anatomy of single-field inflationary models for primordial black holes
• Non-perturbative non-Gaussianity and primordial black holes
• Quantum loop effects on the power spectrum and constraints on primordial black holes
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Galileon inflation evades the no-go for PBH formation in the single-field framework
• No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
• Primordial black holes from single-field inflation: a fine-tuning audit
• Stochastic constant-roll inflation and primordial black holes
• Primordial non-Gaussianity from ultra slow-roll Galileon inflation
• Scalar induced gravity waves from ultra slow-roll Galileon inflation
• Primordial non-Gaussianity as a saviour for PBH overproduction in SIGWs generated by Pulsar Timing Arrays for Galileon inflation
• Realisation of the ultra-slow roll phase in Galileon inflation and PBH overproduction
• Numerical simulations of stochastic inflation using importance sampling
• Large fluctuations and Primordial Black Holes
• Numerical stochastic inflation constrained by frozen noise
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Stochastic Inflation in General Relativity
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Smooth coarse-graining and colored noise dynamics in stochastic inflation
• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• 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
• Computing First-Passage Times with the Functional Renormalisation Group
• Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Itô, Stratonovich, and zoom-in schemes in stochastic inflation
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• Eternal inflation near inflection points: a challenge to primordial black hole models
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond