We present a review on some of the basic aspects concerning quantum cosmology in the
presence of cut-off physics as it has emerged in the literature during the last fifteen years …

This Chapter provides an up to date, pedagogical review of some of the most relevant
advances in loop quantum cosmology. We review the quantization of homogeneous …

The occurrences of singularities where spacetime curvature becomes infinite and geodesic
evolution breaks down are inevitable events in classical general relativity (GR) unless one …

Due to the numerical complexities of studying evolution in an anisotropic quantum
spacetime, in comparison to the isotropic models, the physics of loop quantized anisotropic …

Resolution of singularities in the Kantowski–Sachs model due to non-perturbative quantum
gravity effects is investigated. Using the effective spacetime description for the improved …

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX
spacetime in two different quantizations—the connection operator based'A'quantization and …

Generic resolution of singularities and geodesic completeness in the loop quantization of
Bianchi-II spacetimes with arbitrary minimally coupled matter is investigated. Using the …

The spatially closed Friedmann-Lemaître-Robertson-Walker model in loop quantum
cosmology admits two inequivalent consistent quantizations: one based on expressing the …

We study solutions to the effective equations for the Bianchi IX class of spacetimes within
loop quantum cosmology (LQC). We consider Bianchi IX models whose matter content is a …

We present a list of open questions in mathematical physics. After a historical introduction, a
number of problems in a variety of different fields are discussed, with the intention of giving …