Quantum Mechanical Formulation Of Quantum Cosmology For Brane-World Effective Action

TL;DR

This paper develops a quantum cosmology framework for the Brane-World effective action with higher order curvature terms, deriving a Schrödinger-like equation and demonstrating a consistent quantum probability interpretation.

Contribution

It introduces a canonical quantization approach for the Brane-World effective action with higher curvature invariants, leading to a hermitian Hamiltonian and a quantum mechanical interpretation.

Findings

Derivation of a Schrödinger-like equation for the model

Hermitian effective Hamiltonian ensures probability conservation

Classical solutions recover Einstein's equations

Abstract

Canonical quantization of the Brane-World effective action presented by Kanno and Soda containing higher order curvature invariant terms, has been performed. It requires introduction of an auxiliary variable. As observed in a series of publications by Sanyal and Modak, here again we infer that properly chosen auxiliary variable leads to a Schrodinger like equation where the kinetic part of a canonical variable disentangles from the rest of the variables giving a natural quantum mechanical flavour of time. Further, the effective Hamiltonian turns out to be hermitian, leading to the continuity ewuation. Thus, a quantum mechanical probability inter pretation is plausible. Finally, the extremization of the effective potential leads to Einstein's equation and a well behaved classical solution, which is a desirable feature of the gravitational action containing higher order curvature invariant terms.