Inflationary stochastic anomalies

Understand

The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory.

• It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability distribution function of the fields, and possibly their momenta.
• The link between these two descriptions is ambiguous in general, as it depends on an implicit discretisation procedure, the two prominent ones being the It\^o and Stratonovich prescriptions.
• Here we show that the requirement of general covariance under field redefinitions is verified only in the latter case, however at the expense of introducing spurious `frame' dependences.