Canonical and Quantum FRW Cosmological Solutions in M-theory
We present a 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 diagonalize the Hamiltonian. We find the observables and discuss in detail the phase space of the classical theory. In particular, a region of 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 always contracts. We find the quantum solutions of the model and obtain the positive norm Hilbert space of states. Finally, the correspondence between wavefunctions and classical solutions is outlined.
M. Cavaglia and P. V. Moniz, "Canonical and Quantum FRW Cosmological Solutions in M-theory," Classical and Quantum Gravity, vol. 18, no. 1, pp. 95 - 120, Institute of Physics - IOP Publishing, Jan 2001.
The definitive version is available at https://doi.org/10.1088/0264-9381/18/1/307
FCT (Fundação para a Ciência e Tecnologia)
United States. Department of Energy
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© 2001 Institute of Physics - IOP Publishing, All rights reserved.
01 Jan 2001
This work is supported by grants ESO/PROJ/1258/98, CERN/P/FIS/15190/1999, Sapiens-Proj32327/99. MC is partially supported by the FCT grant Praxis XXI BPD/20166/99. This work is supported in part by funds provided by the US Department of Energy (DOE) under cooperative research agreement DE-FC02-94ER40818