Unlike in isotropic models, we now have inverse powers of , even in the vacuum case, through the spin connection, unless we are in the Bianchi I model. This is a consequence of the fact that not just extrinsic curvature, which in the isotropic case is related to the matter Hamiltonian through the Friedmann equation, leads to divergences but also intrinsic curvature. These divergences are cut off by quantum geometry effects as before, such that the dynamical behavior also changes. This can again be dealt with by phenomenological equations where inverse powers of triad components are replaced by bounded functions . However, even with those corrections, expressions for curvature are not necessarily bounded unlike in the isotropic case. This comes from the presence of different classical scales, , such that more complicated expressions as in are possible, while in the isotropic model there is only one scale and curvature can only be an inverse power of , which is then regulated by effective expressions like .
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 2.0 Germany License.