Stationary Phase Approximation and Instanton-like States for Cosmological In-In Path Integrals

The path integral, which generates in-in correlation functions of a scalar field in a cosmological spacetime, is shown to admit nontrivial classical solutions as stationary phases. Although the solutions exist for Lorentzian signature, their contribution to the path integral is reminiscent that of the instantons in Euclidean field theories. When the scalar potential has more than one locally stable vacua, the correlation functions receive contributions from all of them via these instanton-like configurations, which is similar to tunneling. We present some explicit solutions for toy models and discuss possible implications of our results.