Quantum Cosmology and structure formation in the Universe

Open Access
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
May 23, 2008
Committee Members:
  • Martin Bojowald, Committee Chair
  • Abhay Vasant Ashtekar, Committee Member
  • Stephon Alexander, Committee Member
  • Leonid Berlyand, Committee Member
  • loop quantum gravity
  • loop quantum cosmology
  • cosmological structure formation
  • effective theories
  • cosmological perturbation theory
This thesis consists of two major parts both belonging to the field of Loop Quantum Gravity (LQG). In the first part (chapters 1-3), we restrict ourselves to the case of homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model of the Universe which lies within the domain of Loop Quantum Cosmology (LQC). The goal is to investigate the robustness of phenomenological implications of LQC based on an alternative (Plebanski) model of the gravitational action (chapter 1). In the two following chapters we study models with matter represented by a non-minimally coupled scalar field. In that context, we show possibility of successful loop quantum corrected inflation and extend the singularity removal mechanism to non-minimal models. In the second part of the thesis (4-8), we investigate evolution of cosmological perturbations using canonical formalism of LQG. We start with presenting Einstein's equations linearized around a flat FRW background taking into account loop quantum effects that should be expected in the simplest case of diagonal metric perturbations. Applications here are corrections to the Newton potential and to the evolution of large scale matter density fluctuations potentially noticeable in a running spectral index. We proceed with a detailed derivation of the perturbed effective equations, assuming implicit quantum corrections expected from LQG, and present one example of how effective constraints generating these equations can be obtained explicitly. At the end (chapters 7 and 8) we extend the analysis to generic (non-gauge-fixed) metric perturbations systematically investigating anomaly-free conditions for general quantum corrections. We conclude presenting gauge-invariant cosmological perturbation equations taking into account allowed quantum corrections. Each chapter is rather self-contained and can be read independently of the others. Although, the reader is encouraged to read the last two chapters together, as the splitting was mostly done for aesthetical reasons.