### 4.13 Anisotropy: Phenomenological higher curvature

As in isotropic models, the discreteness of geometry also provides corrections of higher powers of
extrinsic curvature components, and these can take different forms depending on how the discreteness of an
underlying state changes during evolution. Due to the larger number of degrees of freedom, there are now
more options for the behavior and a larger variety of potential phenomena. Viable classes of discretization
effects are, however, rather strongly restricted by the requirement of showing the correct semiclassical
behavior in the right regimes [75, 128]. Thus, even without developing a precise relation between a full
Hamiltonian constraint and the effects it implies for the refinement in a model, one can self-consistently test
symmetric models, although only initial steps [127, 126, 125] toward a comprehensive analysis have been
undertaken.
Anisotropic solutions as analogs for Kasner solutions in the presence of higher powers of extrinsic
curvature have first been studied in [142], although without considering refinements of the discreteness
scale. These solutions have already shown that anisotropic models also exhibit bounces when such
corrections are included phenomenologically, i.e., disregarding quantum backreaction. The issue
has been revisited in [128, 42] for models including refinement (and a free, massless scalar as
internal time) with the same qualitative conclusions. Similar calculations have been applied to
Kantowski–Sachs models, which classically provide the Schwarzschild interior metric, without refinement
in [231, 232] and with two different versions of refinement in [42]. They can thus be used to obtain
indications for the behavior of quantum black holes, at least in the vacuum case. Then, however, one
cannot use the arguments, which in isotropic cosmological models allowed one to conclude that
higher-power corrections are dominant given a large matter content. Correspondingly, bounces of
the higher-power phenomenological equations happen at much smaller scales than in massive
isotropic models. They are thus less reliable because other corrections can become strong in those
regimes.