Multifield stochastic inflation: Relevance of number of fields in statistical moments

TL;DR

This paper investigates how the number of scalar fields affects stochastic inflationary predictions, deriving general formulas for statistical moments and discussing bounds on field numbers.

Contribution

It provides the first analytical formulas for higher-order moments of the stochastic number of e-folds in multifield inflation, explicitly depending on the number of fields.

Findings

Derived a general formula for higher-order moments of e-folds.

Showed the dependence of statistical quantities on the number of fields.

Established an upper bound on the number of fields for successful inflation.

Abstract

In multifield inflation driven by $d$ scalar fields, $O (d)$ symmetry renders the number of fields irrelevant at classical level. This ceases to be the case once stochastic effects are accommodated. The statistical quantities such as the mean number and the variance of $e$-folds as well as the primordial power spectrum and its scale dependence are perturbatively calculated in a small-noise regime. In particular, a general formula is derived for arbitrary higher-order statistical moments of the stochastic number of $e$-folds at all perturbative orders, keeping the dependence on the number of fields fully analytical. It is also discussed that the requirement for inflation to be successfully terminated puts a theoretical bound on the number of fields from above. Those general results are demonstrated for several $O (d)$-symmetric models.