Doctor of Philosophy (PhD)
Department of Physics and Astronomy
Loop quantum cosmology (LQC) has in recent years led to successful resolution of singularities in cosmological models while agreeing with general relativity in low curvature limit. Existence of a bounce and the possibility of an effective continuum description closely approximating the quantum evolution have been notable features of this singularity resolution. The effective spacetimes of loop quantized isotropic and Bianchi-I models have been shown to be geodesically complete and free from strong singularities. In this dissertation, we extend these results to effective loop quantized Bianchi-II, Bianchi-IX and Kantowski--Sachs models with arbitrary minimally coupled matter, and also explore the possibility of symmetric bounces in loop quantized black hole interiors. These are anisotropic spacetimes with spatial curvature. For models with both anisotropy and spatial curvature, earlier techniques to loop quantize the isotropic and Bianchi-I models do not work. Using holonomies along open edges, two quantizations of these models are available in literature - the Ashtekar connection based `A' quantization and the extrinsic curvature based `K' quantization. Considering the effective dynamics of both these quantizations in the Bianchi-II model, we show that the scale factors and the volume remains non-zero and finite for all finite time evolution. Though the energy density, the expansion and shear scalars are bounded, some curvature invariants may potentially diverge. However, geodesic evolution remains regular at such potential divergences and no strong singularities are present. In comparison to the `K' quantization, the `A' quantization in Bianchi-II requires to either impose weak energy conditions (WEC) or include inverse triad corrections to obtain these results. We then show singularity resolution in Bianchi-IX model in both these quantizations. However, now inverse triad corrections must be included in the `A' quantization as WEC are insufficient for singularity resolution. We prove singularity resolution in effective Kantowski--Sachs model with matter without needing inverse triad corrections, where `A' and `K' quantizations are equivalent due to special symmetries. Finally, using an analysis based on Dirac observables of the vacuum effective Kantowski--Sachs spacetime as a model for the Schwarzschild interior, we obtain a symmetric bounce condition, and analyze implications of different dynamical prescriptions giving symmetric bounces.
Saini, Sahil, "Singularity Resolution in Anisotropic and Black Hole Spacetimes in Loop Quantum Cosmology" (2018). LSU Doctoral Dissertations. 4775.