  The paper deals with a suitable transformation related to the metric scalar
of the hyper-surface so that the Raychaudhuri Equation (RE) can be written as a
second order nonlinear differential equation. A first integral of this second
order differential equation gives a possible analytic solution of the RE. Also,
it is shown that construction of a Lagrangian (and hence a Hamiltonian) is
possible, from which the RE can be derived. Wheeler-Dewitt equation has been
formulated in canonical quantization scheme and norm of it's solution (wave
function of the universe) is shown to affect the singularity analysis in the
quantum regime for any spatially homogeneous and isotropic cosmology. Finally
Bohmian trajectories are formulated with causal interpretation and these
quantum trajectories unlike classical geodesics obliterate the initial big-bang
singularity when the quantum potential is included.
