Semiclassical Limit and Time in Quantum Cosmology

TL;DR

This paper introduces a method to extract the classical time evolution of the universe from quantum cosmology wave functions, bridging quantum and classical descriptions by analyzing the Wheeler-DeWitt equation.

Contribution

It presents a novel approach to recover classical dynamics and time in quantum cosmology by using the Hamilton-Jacobi function derived from the wave function.

Findings

Successfully recovers classical solutions from quantum wave functions.

Provides a framework to include quantum corrections in cosmological models.

Clarifies the role of the semiclassical limit in quantum cosmology.

Abstract

We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function $W$ as the imaginary part of the $\ln \Psi$ we can recover the classical solution, and quantum corrections. The key idea is to let the energy of the Wheeler-DeWitt equation vanish only after the semiclassical limit is taken.