Speaker
Description
Based on ArXiv 2504.17680, B. Blachier, C. Ringeval (2025)
Cosmic inflation may exhibit stochastic periods during which quantum fluctuations dominate over the semi-classical evolution. Extracting observables in these regimes is a notoriously difficult program as quantum randomness makes them fully probabilistic. However, among all the possible quantum histories, the ones which are relevant for Cosmology are conditioned by the requirement that stochastic inflation ended. From an observational point of view, it would be more convenient to model stochastic periods as starting from the time at which they ended and evolving backwards in times. In some cases, it is even compulsory to compute observables with respect to local observers in order to avoid gauge artefacts.
We present a time-reversed approach to stochastic inflation, based on a reverse Fokker-Planck equation, which allows us to derive non-perturbatively the probability distribution of the field values at a given time before the end of the quantum regime. As a motivated example, we solve the flat semi-infinite potential and express the probability distribution of the quantum-generated curvature fluctuations. We show that even when allowing eternal inflation to occur, the reverse-time scheme cure divergences: the probability distribution is finite, exhibits heavy tails and some features of Gaussian statistics are recovered for small curvature perturbations. This reverse-time stochastic $\delta N$-formalism enables a path-by-path conditioning by the lifetimes of the stochastic trajectories, and express probabilities in number of $e$-folds in reference to the end of inflation hypersurface, hence it could be applied to any inflationary potentials and quantum diffusion eras, including the ones leading to the formation of primordial black holes.
