Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity
(LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role …

Quantum gravity is expected to be necessary in order to understand situations in which
classical general relativity breaks down. In particular in cosmology one has to deal with …

We compute the transition amplitude between coherent quantum states of geometry peaked
on homogeneous-isotropic metrics. We work in the context of pure gravity without matter, we …

This introductory review is addressed to beginning researchers. Some of the distinguishing
features of loop quantum gravity are illustrated through loop quantum cosmology of FRW …

The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic
model was recently constructed. In this paper, the methods are extended to the anisotropic …

A general class of loop quantizations for anisotropic models is introduced and discussed,
which enhances loop quantum cosmology by relevant features seen in inhomogeneous …

Several examples are known where quantum gravity effects resolve the classical big bang
singularity by a bounce. The most detailed analysis has probably occurred for loop quantum …

Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general
relativity simplify in their reduced form some of the mathematical ingredients of black hole or …

A direct correspondence of quantum mechanics as a minisuperspace model for a self-
interacting scalar quantum-field theory is established by computing, in several models, the …

We develop a gauge-invariant canonical perturbation scheme for perturbations around
symmetry-reduced sectors in generally covariant theories, such as general relativity. The …