Probability of Boundary Conditions in Quantum Cosmology

TL;DR

This paper numerically evaluates the probabilities of different boundary conditions for the wave function of the universe in quantum cosmology, favoring tunneling conditions and identifying a unique boundary condition under certain parameters.

Contribution

It introduces a method to specify and evaluate probabilities of boundary conditions using exact solutions of the Wheeler-DeWitt equation with scalar fields.

Findings

Probability distribution favors tunneling boundary condition.

For large parameters, a unique boundary condition different from tunneling is selected.

Numerical solutions support boundary condition proposals in quantum cosmology.

Abstract

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler-DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.