Critical Number of Fields in Stochastic Inflation

TL;DR

This paper investigates how multiple fields in stochastic inflation influence the statistical properties of inflationary e-folds, revealing critical thresholds for field numbers and potential for large quantum corrections in multi-field models.

Contribution

It introduces a novel analysis of stochastic effects in multi-field inflation using first passage time techniques, highlighting the critical number of fields and regularization methods for infinite correlation functions.

Findings

Number of fields critically affects inflationary dynamics.

Multi-field models can produce large stochastic corrections at sub-Planckian energies.

Regularization with a reflecting wall yields well-defined correlation functions.

Abstract

Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary $e$-folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic $\delta N$ formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes non-vanishing when more than two fields are driving inflation. The mean number of $e$-folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularised if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well-defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multi-field models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.