Quantum Gravity of a Brane-like Universe

TL;DR

This paper formulates a quantum gravity model for a brane-like universe, deriving a Wheeler-DeWitt-like equation using a novel Lagrange multiplier approach within the Regge-Teitelboim embedding framework.

Contribution

It introduces a new Lagrange multiplier method to derive a quadratic Hamiltonian and a Wheeler-DeWitt-like equation for brane-world quantum gravity.

Findings

Derivation of a Wheeler-DeWitt-like equation for brane universe

Introduction of a novel Lagrange multiplier approach

Approach to Einstein limit in quantum gravity model

Abstract

Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism is carried out. Invoking a novel Lagrange multiplier, accompanying the lapse function and the shift vector, we derive the quadratic Hamiltonian and the corresponding bifurcated Wheeler-Dewitt-like equation. The inclusion of arbitrary matter resembles minimal coupling.