  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.
