We extend recent discussions of singularity avoidance in quantum gravity from isotropic to anisotropic cosmological models. The investigation is done in the framework of quantum geometrodynamics (Wheeler–DeWitt equation). We formulate criteria of singularity avoidance for general Bianchi class A models and give explicit and detailed results for Bianchi I models with and without matter. The singularities in these cases are big bang and big rip. We find that the classical singularities can generally be avoided in these models.

Germany

Claus Kiefer

Nick Kwidzinski

Dennis Piontek

Singularity avoidance in Bianchi I quantum cosmology

We present an analysis of the Kretschmann and Weyl squared scalars for the general Bianchi IX model filled with tilted dust. Particular attention is given to the asymptotic regime close to the singularity for which we provide heuristic considerations supported by numerical simulations. The present paper is an extension of our earlier publication (Kiefer et al., in Eur Phys J C 78:691, 2018).

Poland

Włodzimierz Piechocki

Curvature invariants for the Bianchi IX spacetime filled with tilted dust

We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we use the Hubble normalized ones commonly applied in the examination of the dynamics of homogeneous models. Applying the dynamical systems method leads to the result that in both cases the continuous space of critical points is higher dimensional and they are of the nonhyperbolic type. This is a generic feature of the dynamics of both cases and seems to be independent on the choice of phase space variables. The topologies of the corresponding critical spaces are quite different. We conjecture that the nondiagonal case may carry a new type of chaos different from the one specific to the usually examined diagonal one.

Ewa Czuchry

Comparing the dynamics of diagonal and general Bianchi IX spacetime

We show that the complex dynamics of the general Bianchi IX universe in the vicinity of the spacelike singularity can be approximated by a simplified system of equations. Our analysis is mainly based on numerical simulations. The properties of the solution space can be studied by using this simplified dynamics. Our results will be useful for the quantization of the general Bianchi IX model.