Inflationary Quantum Cosmology: General Framework and Exact Bianchi I Solution

TL;DR

This paper develops a quantum cosmological framework for inflationary homogeneous universes using loop quantum gravity, providing an exact Bianchi I solution and exploring its implications for quantum states and the universe's scale factor.

Contribution

It introduces a new quantum framework for inflationary Bianchi I models using Ashtekar variables and derives an exact semi-classical solution within this setting.

Findings

Exact classical Bianchi I solution obtained

Semi-classical quantum state also an exact solution

Quantum scale factor has a continuous spectrum

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.