Absence of the Kasner singularity in the effective dynamics from loop quantum cosmology

In classical general relativity, the generic approach to the initial singularity is usually understood in terms of the Belinskii-Khalatnikov-Lifschitz scenario. In this scenario, along with the Bianchi IX model, the exact, singular, Kasner solution of the vacuum Bianchi I model also plays a pivotal role. Using an effective classical Hamiltonian obtained from loop quantization of the vacuum Bianchi I model, an exact solution is obtained which is nonsingular due to a discreteness parameter. The solution is parametrized in exactly the same manner as the usual Kasner solution and reduces to the Kasner solution as the discreteness parameter is taken to zero. At the effective Hamiltonian level, the avoidance of Kasner singularity uses a mechanism distinct from the “inverse volume” modifications characteristic of loop quantum cosmology.