New Asymptotic Expanstion Method for the Wheeler-DeWitt Equation

TL;DR

This paper introduces a novel asymptotic expansion technique for the Wheeler-DeWitt equation, enabling a complete separation into matter and gravitational components, with applications to the FRW universe.

Contribution

The paper develops a new asymptotic expansion method that fully separates the Wheeler-DeWitt equation and accounts for quantum back-reaction, valid across all superspace regions.

Findings

Successfully separates matter and gravity equations in the asymptotic limit

Derives higher order quantum corrections for gravity

Demonstrates applicability to the minimal FRW universe

Abstract

A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$ approaching infinity. The higher order quantum corrections of the gravity to the matter field are found. The new asymptotic expansion method is valid throughout all regions of superspace compared with other expansion methods with a certain limited region of validity. We apply the new asymptotic expansion method to the minimal FRW universe.