Abstract:
This thesis presents some studies on the Loop Quantization of cosmological models. The effect of loop quantization of FRW cosmology in the context of effective equations and WKB approximation are studied in the first part of the thesis. The initial steps undertaken in the second part, in construction of 'A Loop Quantized theory' of a midi-superspace model known as the Gowdy Model on T^3. One of the qualitatively distinct and robust implication of Loop Quantum Gravity - the underlying discrete structure is manifested by the Hamiltonian Constraint Equation, in the cosmological context elucidated by Loop Quantum Cosmology. An alternative derivation of the effective Hamiltonian is presented, by-passing the continuum approximation step. The Kinematical Hilbert Space is introduced on which the appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is straightforward. Imposition of the Gauss constraint can be done on the Kinematical Hilbert Space to select subspace of gauge invariant states. The quantization of the Hamiltonian constraint is carried out, making specific choices. Alternative choices are briefly discussed. It appears that to get spatial correlations reflected in the Hamiltonian constraint, one may have to adopt the so called 'effective operator view point'.
