Inflationary stochastic anomalies

摘要: The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical theory. It is usually formulated in terms Langevin equations, giving rise to Fokker-Planck equation for probability distribution function fields, and possibly their momenta. link between these two descriptions ambiguous general, as it depends on an implicit discretisation procedure, prominent ones being Ito Stratonovich prescriptions. Here we show that requirement general covariance under field redefinitions verified only latter case, however expense introducing spurious `frame' dependences. This anomaly disappears when there one source stochasticity, like slow-roll single-field inflation, but manifests itself taking into account full phase space, or presence multiple fields. Despite difficulties, use physical arguments write down covariant describes diffusion light scalar non-linear sigma models overdamped limit. We apply test de Sitter space some statistical properties class two-field with derivative interactions can be reproduced using correspondence model endowed effective potential. also present explicit results simple extension $\lambda \phi^4$ theory hyperbolic geometry. difficulties describe seem counterparts notoriously difficult problem maintaining theories, related choices operator ordering path-integral constructions. Our work thus opens new avenues research crossroad cosmology, physics,