paper

Inflationary Quantum Cosmology: General Framework and Exact Bianchi I Solution

arXiv:gr-qc/0407114 · doi:10.1103/PhysRevD.70.084040

Abstract

Using the methods of loop quantum gravity, we derive a framework for describing an inflationary, homogeneous universe in a purely quantum theory. The classical model is formulated in terms of the Ashtekar-Sen connection variables for a general subclass of Bianchi class A spacetimes. This formulation then provides a means to develop a corresponding quantum theory. An exact solution is derived for the classical Bianchi type I model and the corresponding semi-classical quantum state is found to also be an exact solution to the quantum theory. The development of a normalizable quantum state from this exact solution is presented and the implications for the normalizability of the Kodama state discussed. We briefly consider some consequences of such a quantum cosmological framework and show that the quantum scale factor of the universe has a continuous spectrum in this model. This result may suggest further modifications that are required to build a more accurate theory. We close this study by suggesting a variety of directions in which to take the results presented.

24 pages, submitted to Phys. Rev. D; v2: modifications to some formulae; v3: Poisson bracket calculation corrected

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