Stochastic inflation in compact extra dimensions

L. Lorenz, J. Martin, J. Yokoyama

Inflationary scenarios based on string theory have become more viable and increasingly popular in recent years. For example, in "brane inflation" the geometric interpretation of the inflaton field can be exploited to derive consistency conditions on the inflaton potential's parameters. However, because of its quantum nature, the inflaton field is subject to stochastic quantum jumps on top of its classical motion downwards on the potential. The impact of these jumps can be modelled by a noise term in the Langevin equation that describes inflation in the slow roll limit. We solve this Langevin equation for an inflaton field with Dirac Born Infeld (DBI) kinetic term (which typically arises in brane inflationary scenarios) and use the result to determine the field value's Probability Density Function (PDF). It is important to check that these stochastic modifications to the field trajectory are still consistent with the string theoretic model building ingredients. In particular, in brane inflation the inflaton corresponds to a distance within the compact extra dimensions of string theory, and these dimensions' finite size therefore restricts the accessible field values. We argue that in a consistent stochastic approach the distance-inflaton's PDF must vanish for geometrically forbidden field values and discuss potential observable consequences.