Aspects of Quantum Cosmology

TL;DR

This thesis demonstrates that anisotropic quantum cosmological models can achieve unitary evolution through self-adjoint Hamiltonians, and confirms the quantum equivalence of Jordan and Einstein frames across multiple models.

Contribution

It shows how to attain unitarity in anisotropic models and establishes quantum frame equivalence for various cosmological models, extending previous understanding.

Findings

Hamiltonians admit self-adjoint extensions enabling unitarity

Quantum equivalence of Jordan and Einstein frames confirmed

Unitarity preserves Noether symmetry but affects scale invariance

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.