Multiple Fields in Stochastic Inflation
Abstract
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary -folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of -folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of -folds can be used to calculate the distribution of primordial density perturbations in the stochastic- formalism.
Keywords
Cite
@article{arxiv.1604.04502,
title = {Multiple Fields in Stochastic Inflation},
author = {Hooshyar Assadullahi and Hassan Firouzjahi and Mahdiyar Noorbala and Vincent Vennin and David Wands},
journal= {arXiv preprint arXiv:1604.04502},
year = {2016}
}
Comments
20 pages without appendices (total 30 pages), 5 figures, 1 table. matches published version in JCAP (references added)