On Hamiltonian formulation of cosmologies

Novello er al [1,2] have shown that it is possible to find a pair of canoni cally conjugate variables (written in terms of gauge-invariant variables) s o as to obtain a Hamiltonian that describes the dynamics of a cosmological system. This opens up the way to the usual technique of quantization. Elbaz et al [4] have applied this method to the Hamiltonian formulation of FRW c osmological equations. This note presents a generalization of this approach to a variety of cosmologies. A general Schrodinger wave equation has been derived and exact solutions have been worked out for the stiff matter era f or some cosmological models. It is argued that these solutions appear to hi nt at their possible relevance in the early phase of cosmological evolution .