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Abstract: Stochastic effects during inflation can be addressed by averaging the quantuminflaton field over Hubble-patch sized domains. The averaged field then obeys aLangevin-type equation into which short-scale fluctuations enter as a noiseterm. We solve the Langevin equation for a inflaton field with Dirac BornInfeld DBI kinetic term perturbatively in the noise and use the result todetermine the field value-s Probability Density Function PDF. In thiscalculation, both the shape of the potential and the warp factor are arbitraryfunctions, and the PDF is obtained with and without volume effects due to thefinite size of the averaging domain. DBI kinetic terms typically arise instring-inspired inflationary scenarios in which the scalar field is associatedwith some distance within the compact extra dimensions. The inflaton-saccessible range of field values therefore is limited because of the extradimensions- finite size. We argue that in a consistent stochastic approach thedistance-inflaton-s PDF must vanish for geometrically forbidden field values.We propose to implement these extra-dimensional spatial restrictions into thePDF by installing absorbing or reflecting walls at the respective boundariesin field space. As a toy model, we consider a DBI inflaton between twoabsorbing walls and use the method of images to determine its most general PDF.The resulting PDF is studied in detail for the example of a quartic warp factorand a chaotic inflaton potential. The presence of the walls is shown to affectthe inflaton trajectory for a given set of parameters.

Autor: Larissa Lorenz, Jerome Martin, Jun'ichi Yokoyama


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