Manifestly covariant theory of stochastic inflation
DrYuichiro Tada(Nagoya University)
The stochastic approach to inflation can non-perturbatively treat the superhorizon fluctuations as the classical random noise to go beyond the standard perturbative QFT approach. I first review how this approach enables us to calculate the observable curvature perturbations in a non-perturbative way and how it can be implemented in a numerical program. I then describe the covariance of the stochastic theory and the discretization scheme of the stochastic noise, which are important both theoretically and practically. Mathematically the stochastic noise can be discretized in an arbitrary manner, but we reveal the physically motivated discretization, which ensures the covariance of the stochastic theory on the inflatons' target manifold.