Aspects of Quantum Cosmology

Pandey, Sachin (2020) Aspects of Quantum Cosmology. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Sachin Pandey (13IP016)) 13IP016.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

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 used the dynamical variable related to the fluid as a time parameter following Schutz’s formalism. 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 obtained finite normed and time independent wave packet showing the unitary evolution of the models. Expectation values of scale factors showed that the quantized model avoids the problem of singularity. We also showed that unitarity of the model preserves the Noether symmetry but loses the scale invariance. Using the Wheeler-DeWitt quantization scheme, we showed the equivalence of Jordan and Einstein frames at the quantum level. We quantized the Brans-Dicke theory in both the frames for the flat FRW model using dynamical variable related to the scalar field as a time parameter. 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.

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