Stochastic inflation at all order in slow-roll parameters: foundations

Understand

In this paper we develop the formalism for the stochastic approach to inflation at all order in slow-roll parameters.

• This is done by including the momentum and Hamiltonian constraints into the stochastic equations.
• We then specialise to the widely used Starobinski approximation where interactions between IR and UV modes are neglected.
• We show that, whenever this approximation holds, no significant deviations are observed when comparing the two-point correlation functions (power spectrum) calculated with stochastic methods, to the ones calculated with the QFT approach to linear theory.