Aspects of Quantum Cosmology

Abstract

In this thesis, we try to resolve the alleged problem of non-unitarity for various anisotropic cosmological models. Using Wheeler-DeWitt formulation, we quantized the anisotropic models with variable spatial curvature, namely Bianchi II and Bianchi VI. We showed that Hamiltonian of respective models admits self-adjoint extension, thus unitary evolution. We further extended the unitary evolution for higher dimensional anisotropic cosmological models. We also showed that unitarity of the model preserves the Noether symmetry but loses the scale invariance. In later part of this thesis, we showed the equivalence of Jordan and Einstein frames at the quantum level for the flat FRW model. Obtained expressions for wave packet matched exactly in both the frames indicating the equivalence of frames. We also showed that equivalence holds true for various anisotropic quantum cosmological models, i.e., Bianchi I, V, X, LRS Bianchi-I and Kantowski-Sachs models.

Thesis submitted to IISER Kolkata for the Degree of Doctor of Philosophy in Science, December 2020

References in corpus (7)

• The (pseudo)issue of the conformal frame revisited
• Equivalence of the Einstein and Jordan frames
• The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
• Restoring unitarity in anisotropic quantum cosmological models
• Addressing the issue of non-unitarity in anisotropic quantum cosmology
• Wheeler-DeWitt quantization and singularities
• Dynamics of a perfect fluid through velocity potentials with aplication in quantum cosmology