Time-reversed stochastic inflation in the quantum well
Abstract
Time-reversed stochastic inflation solves the stochastic evolution of the inflationary universe backward in time, by counting the number of e-folds from the end of quantum diffusion towards some initial state. The point of view of observers attached to the end-of-inflation hypersurface is thus enforced. In this work, we exactly solve time-reversed stochastic inflation in a flat and bounded potential, the so-called quantum well. At given lifetime, the field behaviour is found to be either indistinguishable from the one obtained in a semi-infinite flat potential, or, subject to enhanced stochasticity where any memory of the initial state is erased. The derived distribution of curvature perturbations reduces to the semi-infinite result for small fluctuations while it develops exponential tails for the large ones. Such tails arise for both positive and negative values, and decay twice as fast as the one obtained in the standard forward stochastic inflation. These differences may have important consequences for tail-sensitive phenomena, such as primordial black hole formation.
Versions
Related
- Calculating the squeezed bispectrum in stochastic inflation by Monte Carlo simulation
- Elastic boundaries in Stochastic Inflation
- Stochastic scalar-tensor inflation and beyond
- Eigenvalue formulation of Stochastic Inflation and application to large perturbation generating inflationary features
- Connecting the Dots: Prospects for Detecting Multi-Source Inflation through Scale-Dependent and Stochastic Bias of Little Red Dots
BibTeX
@misc{animali2026timereversed,
title = {{Time-reversed stochastic inflation in the quantum well}},
author = {Chiara Animali and Baptiste Blachier and Nanoka Okada and Christophe Ringeval and Tomo Takahashi and Koki Tokeshi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.31323},
eprint = {2605.31323},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.31323},
}
RIS
TY - UNPB
TI - Time-reversed stochastic inflation in the quantum well
AU - Chiara Animali
AU - Baptiste Blachier
AU - Nanoka Okada
AU - Christophe Ringeval
AU - Tomo Takahashi
AU - Koki Tokeshi
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2605.31323
UR - https://arxiv.org/abs/2605.31323
AB - Time-reversed stochastic inflation solves the stochastic evolution of the inflationary universe backward in time, by counting the number of e-folds from the end of quantum diffusion towards some initial state. The point of view of observers attached to the end-of-inflation hypersurface is thus enforced. In this work, we exactly solve time-reversed stochastic inflation in a flat and bounded potential, the so-called quantum well. At given lifetime, the field behaviour is found to be either indistinguishable from the one obtained in a semi-infinite flat potential, or, subject to enhanced stochasticity where any memory of the initial state is erased. The derived distribution of curvature perturbations reduces to the semi-infinite result for small fluctuations while it develops exponential tails for the large ones. Such tails arise for both positive and negative values, and decay twice as fast as the one obtained in the standard forward stochastic inflation. These differences may have important consequences for tail-sensitive phenomena, such as primordial black hole formation.
ER -