Critical Number of Fields in Stochastic Inflation.
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 δN formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing 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 regularized 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, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, United Kingdom.
Vincent
V
Vennin
Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, United Kingdom.|School of Earth and Environmental Sciences, University of Portsmouth, Burnaby Building, Burnaby Road, Portsmouth PO1 3QL, United Kingdom.
Hooshyar
H
Assadullahi
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), Post Office Box 19395-5531, Tehran, Iran.
Hassan
H
Firouzjahi
School of Astronomy, Institute for Research in Fundamental Sciences (IPM), Post Office Box 19395-5531, Tehran, Iran.|Department of Physics, University of Tehran, Post Office Box 14395-547, Tehran, Iran.
Mahdiyar
M
Noorbala
Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, United Kingdom.
David
D
Wands