Canonical and quantum FRW cosmological solutions in M-theory

TL;DR

This paper investigates canonical and quantum cosmological solutions in a four-dimensional FRW model derived from M-theory, analyzing classical phase space, quantum states, and the classical-quantum correspondence.

Contribution

It introduces a detailed phase space analysis and quantum solutions for an M-theory derived FRW model, including new observables and classical-quantum correspondence.

Findings

Existence of a phase space region with a contracting and expanding universe

Quantum solutions with a positive norm Hilbert space

Classical-quantum correspondence outlined

Abstract

We present the canonical and quantum cosmological investigation of a spatially flat, four-dimensional Friedmann-Robertson-Walker (FRW) model that is derived from the M-theory effective action obtained originally by Billyard, Coley, Lidsey and Nilsson (BCLN). The analysis makes use of two sets of canonical variables, the Shanmugadhasan gauge invariant canonical variables and the ``hybrid'' variables which diagonalise the Hamiltonian. We find the observables and discuss in detail the phase space of the classical theory. In particular, a region of the phase space exists that describes a four-dimensional FRW spacetime first contracting from a strong coupling regime and then expanding to a weak coupling regime, while the internal space ever contracts. We find the quantum solutions of the model and obtain the positive norm Hilbert space of states. Finally, the correspondence between wave functions and classical solutions is outlined.