Geometrically Consistent Approach to Stochastic DBI Inflation

Understand

Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch sized domains.

• The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term.
• We solve the Langevin equation for a inflaton field with Dirac Born Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's Probability Density Function (PDF).
• In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain.