Multiple Fields in Stochastic Inflation

Understand

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.