Quantization in cosmology: Studies in Wheeler-DeWitt and path integral methods

Ghosh, Saumya (2025) Quantization in cosmology: Studies in Wheeler-DeWitt and path integral methods. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Saumya Ghosh (14IP041)) 14IP041.pdf - Submitted Version Restricted to Repository staff only Download (6MB)

Abstract

In the last century, after the paradigm shift to general relativity, cosmology has undergone significant developments. One of the major advancements in our understanding of the universe is the ongoing effort to merge quantum mechanics with gravity. The motivation for integrating general relativity into the quantum framework is that it should explain the small-scale structure of the universe as well as account for current observational aspects. There are two main approaches to studying quantum cosmology: the Wheeler-DeWitt equation method and the path integral formulation. In this thesis we have performed studies in both of the formalism to deepen our understanding on the quantum features of the universe. We studied the Wheeler-DeWitt quantization in Bianchi type I anisotropic cosmology with a scalar field minimally coupled with Einstein-Hilbert gravity. We also included a perfect fluid matter sector. Using Schutz’s formalism, we used the dynamics of the fluid matter part to play the role of time. We addressed the alleged issue of non-unitarity for this model. We showed that a proper definition in the self-adjointness relation makes the evolution unitary. This also enabled us to construct a well behaved wave function of the universe which could remove the Big-Bang singularity. Furthermore, we explored the same study for flat FRW model with the fluid matter part modeled as Chaplygin gas. This reinstates the fact that the problem of non-unitarity is not related to anisotropic models only. One can face the same issue in isotropic models for an ill defined self-adjointness relation. We also extended our study for noncommutative minisuperspace coordinates. For a long time in the literature the standard procedure was to follow an Euclidean path integral method stemming from the belief that Lorentzian path integral for gravity may not lead to an well defined result for its oscillating nature. However, the application of the Picard-Lefschetz theory enabled us to study Lorentzian path integral in the Kantowski-Sachs anisotropic cosmology. We studied the Hawking-Hartle no-boundary proposal, which revealed that for large scale structure the main contribution to the transition amplitude comes from a initial condition that tends to conical singularity. A massless scalar perturbation analysis showed that large fluctuations are favored which means if there was any initial fluctuation during the beginning of time then that would flare up at the final boundary.

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