Quantum Cosmology of the Nothing

TL;DR

This paper explores quantum cosmology by analyzing wave functions of the universe, focusing on tunneling phenomena and transitions between different expansion phases using a simplified radiation and cosmological constant model.

Contribution

It introduces a new concept of universe tunneling during a bounce in connection space and derives the wave function of the evanescent wave to estimate tunneling probabilities.

Findings

Wave functions include incident, reflected, and evanescent components.

Tunneling probability is estimated from the evanescent wave's wave function.

The model connects quantum tunneling with cosmological phase transitions.

Abstract

Quantum cosmology uses a wave function to model the universe, but finding solutions for this poses a problem as it is difficult to define the boundary conditions or identify the correct path for a path integral. We begin the discussion by going over various proposals and look at how bubble universe nucleation can be used as an analogy for the tunneling wave function. We review how the Hartle-Hawking wave function and tunneling wave functions are equivalent. This leads into how the transition between the decelerated and accelerated expansion is formulated as a bounce in connection space. This is done in a toy model Universe that contains only radiation and a cosmological constant $\Lambda$. The wave function is a superposition on an incident wave, a reflected wave, and an evanescent wave; when it is constructed from wave packets. Using the toy model, we introduce the new concept of the universe tunneling to a different classical region during this bounce in connection space. This concept is explored by deriving the wave function of the evanescent wave $\psi_{ev}$ in order to calculate $|\psi|^2$ to give an indication of the probability of the universe tunneling to another classical region.