TL;DR
This paper explores the classical and quantum solutions of a Bianchi Type I universe with compact spatial sections, highlighting differences from the infinite case, and includes matter fields and backreaction effects.
Contribution
It provides a detailed analysis of the compact Bianchi Type I model, revealing a richer moduli space and solving the Wheeler-DeWitt equation with matter and backreaction considerations.
Findings
Compact case has a 10-dimensional solution space.
Solutions with dust and cosmological constant are derived.
Quantum tunneling solutions are obtained using Vilenkin's boundary condition.
Abstract
The minisuperspace model of a Bianchi Type I universe with compact spatial sections is investigated. The classical solutions are brought onto a form were the difference between compact and infinite spatial sections are manifest. One of the features of the compact case is that it has a non-trivial moduli space. The solution space of the compact Bianchi Type I universe is 10 dimensional whereas the Kasner solutions only have a 1 dimensional solution space. We also include the classical solutions with dust and a cosmological constant. Solutions to the Wheeler-DeWitt equation are obtained in light of the tunneling boundary proposal by Vilenkin. Backreaction effects from a simple scalar field are also investigated.
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