Tunneling in quantum cosmology: numerical study of particle creation

TL;DR

This paper numerically studies tunneling in quantum cosmology, revealing that matter excitations and back reactions significantly influence the tunneling process, with implications for particle creation during universe transitions.

Contribution

It provides a numerical analysis of the Wheeler--De Witt equation showing matter excitation and back reaction effects in quantum tunneling of the universe, a novel insight compared to traditional quantum mechanics.

Findings

Matter gets excited under the barrier during tunneling.

Back reaction of matter influences the tunneling process.

High momentum particles are copiously created during tunneling.

Abstract

We consider a minisuperspace model for a closed universe with small and positive cosmological constant, filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a tunneling transition through an effective barrier between regions of small and large scale factor. We solve numerically the minisuperspace Wheeler--De Witt equation with tunneling boundary conditions for the wave function of the universe, and find that tunneling in quantum cosmology is quite different from that in quantum mechanics. Namely, the matter degree of freedom gets excited under the barrier, provided its interaction with the scale factor is not too weak, and makes a strong back reaction onto tunneling. In the semiclassical limit of small values of cosmological constant, the matter energy behind the barrier is close to the height of the barrier: the system ``climbs up'' the barrier, and then evolves classically from its top. These features are even more pronounced for inhomogeneous modes of matter field. Extrapolating to field theory we thus argue that high momentum particles are copiously created in the tunneling process. Nevertheless, we find empirical evidence for the semiclassical-type scaling with the cosmological constant of the wave function under and behind the barrier.