Description
In this talk based on arXiv:2008.07497 (from Lucas Pinol, Yuichiro Tada and myself), after an introduction to stochastic inflation, I explain the difficulties and the solution to formulate this theory in a manner that respects covariance under field redefinitions. I do so in the general framework of multifield inflation with a curved field space, taking into account the coupling to gravity as well as the full phase space in the Hamiltonian language. Moreover, I show how to rigorously derive the corresponding Langevin equations using tools of nonequilibrium quantum field theory.
