Hybrid Quantization: From Bianchi I to the Gowdy Model

Understand

The Gowdy cosmologies are vacuum solutions to the Einstein equations which possess two space-like Killing vectors and whose spatial sections are compact.

• We consider the simplest of these cosmological models: the case where the spatial topology is that of a three-torus and the gravitational waves are linearly polarized.
• The subset of homogeneous solutions to this Gowdy model are vacuum Bianchi I spacetimes with a three-torus topology.
• We deepen the analysis of the loop quantization of these Bianchi I universes adopting the improved dynamics scheme put forward recently by Ashtekar and Wilson-Ewing.