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arXiv · 1604.04502

Multiple Fields in Stochastic Inflation

Hooshyar Assadullahi·Hassan Firouzjahi·Mahdiyar Noorbala·Vincent Vennin·David Wands
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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 $e$-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 $e$-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 $e$-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-$δN$ formalism.

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Hooshyar Assadullahi, Hassan Firouzjahi, Mahdiyar Noorbala, Vincent Vennin, David Wands. 2016-08-23. Multiple Fields in Stochastic Inflation. https://doi.org/10.1088/1475-7516%2F2016%2F06%2F043

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