Doctor of Philosophy (PhD)
Physics and Astronomy
A key feature of the singularity resolution in loop quantum cosmology (LQC) is the occurrence of the quantum bounce when the spacetime curvature becomes comparable to the Planck scale. The presence of quantum bounce greatly modifies the dynamics of the early universe and can have important implications for observational signatures. Although the quantum bounce has been previously studied via numerical methods for initial conditions that correspond to large macroscopic universes at late times, a detailed study of the robustness of the quantum bounce for a generic class of initial condition has so far been missing due to severe computational challenges. In the first part of this dissertation, we develop the Chimera scheme, an efficient numerical technique, and study the physics of the quantum bounce in an isotropic and homogeneous spacetime. We find that the quantum bounce is a robust phenomenon and independent of initial conditions, while its quantitative features depend on the quantum fluctuations of the initial state. In addition to these results we present a detailed analysis of the validity of the effective description of LQC, which shows that the effective description remains valid so long as the quantum fluctuations in the state are negligible. These results set the stage to compute finer corrections due to the quantum fluctuations of the spacetime geometry to the observational signatures of LQC. Using the Chimera scheme we also study, for the first time, non-singular evolution in the presence of a negative scalar field potential which gives rise to a cyclic universe. In the second part of the thesis, we focus on the phenomenological aspects of the singularity resolution. We study the transitions of various geometrical structures across the bounce and the effect of the quantum bounce on the inflationary scenario in Bianchi-I spacetime. Using the nonsingular evolution of LQC we also explore the possibility of anti-de Sitter to de Sitter vacuum transitions, a long standing problem in the multiverse scenario, which plays an important role in defining a local measure in the multiverse.
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Gupt, Brajesh Kumar, "Some Numerical and Phenomenological Studies in Loop Quantum Cosmology" (2014). LSU Doctoral Dissertations. 1075.