Analyzing Loop Quantum Cosmology of Bianchi I, II, and IX Space with Numerical Methods
University of New Brunswick
In previous literature effective Hamiltonian equations have been generated capturing lead order loop quantum gravity effects for the anisotropic vacuum Bianchi I, II, and IX spaces. Additionally, analytical transition rules have been derived for these spaces governing their rates of expansion and contraction. In this paper, these systems are evolved numerically using high-order Runge-Kutta methods and the transition rules are both tested for these Bianchi spaces and used to categorize loop quantum gravity bounces in Bianchi IX. It is found that these transition rules can predict how the Kasner exponents behave in Bianchi II if neither the potential effects and quantum effects become significant simultaneously. Additionally, the loop quantum gravity bounces in Bianchi IX were able to be sorted into four separate classifications based on these transition rules.