Particle Production from Geometric Transition in Expanding Universe

Abstract

Hawking radiation in a black hole, Gibbons-Hawking radiation in a de Sitter space, and Schwinger mechanism in a constant electric field are the most prominent particle production from the vacuum. The out-vacuum may be superposed of multi-particle states of the in-vacuum and their amplitudes square is the probability for those particles to be spontaneously created from the vacuum [1]. The phase-integral method, one of tunneling pictures, provides the probability for scattering over a barrier and penetration under a well, which give a physical intuition behind pair production [2, 3]. Recently it has been proposed that particle production may be understood by extending the quantum evolution to the complex plane of time in the in-in formalism [4]. The idea is that the geometric contributions from the poles of an analytic Hamiltonian in the complex plane are responsible for not only particle production but also the Stokes phenomenon in de Sitter radiation [5]. In this paper we elaborate further and apply the geometric interpretation of particle production to expanding universes.