Stochastic tunneling in de Sitter spacetime

The formulation of tunneling in real time formalism is discussed. In the case of de Sitter spacetime, there is a method called the stochastic approach, which is known to reproduce the tunneling predicted by Hawking and Moss in the imaginary time formalism. In the case of accelerated expansion of space, the short-wavelength modes are stretched and transformed into long-wavelength modes. In the stochastic approach, such UV-IR transition is incorporated as quantum noise, and the dynamics of the long-wavelength modes are described by stochastic differential equations.

In this talk, we construct a Schwinger-Keldysh path integral that reproduces this stochastic differential equation and reformulate the tunneling probability. We also reproduce the Hawking-Moss tunneling probabilities by using the saddle point approximation.