Canonical and quantum FRW cosmological solutions in M-theory

We present a canonical and quantum cosmological investigation of a spatiall y flat, four-dimensional Friedmann-Robertson-Walker (FRW) model that is der ived from the M-theory effective action obtained originally by Billyard, Co ley, Lidsey and Nilsson (BCLN). The analysis makes-use of two sets of canon ical variables, the Shanmugadhasan gauge-invariant canonical variables and the 'hybrid' variables which diagonalize the Hamiltonian. We find the obser vables and discuss in detail the phase space of the classical theory. In pa rticular, a region of phase space exists that describes a four-dimensional FRW spacetime first contracting from a strong-coupling regime and then expa nding to a weak-coupling regime, while the internal space always contracts. We find the quantum solutions of the model and obtain the positive norm Hi lbert space of states. Finally, the correspondence between wavefunctions an d classical solutions is outlined.