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 …

Cosmological perturbations are generally described by quantum fields on (curved but)
classical space-times. While this strategy has a large domain of validity, it can not be justified …

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 …

A fully consistent linear perturbation theory for cosmology is derived in the presence of
quantum corrections as they are suggested by properties of inverse volume operators in …

A systematic approach is developed in order to obtain spherically symmetric
midisuperspace models that accept holonomy modifications in the presence of matter fields …

Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based
on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the …

A consistent implementation of quantum gravity is expected to change the familiar notions of
space, time, and the propagation of matter in drastic ways. This will have consequences on …

An exactly solvable bounce model in loop quantum cosmology is identified which serves as
a perturbative basis for realistic bounce scenarios. Its bouncing solutions are derived …

Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang
singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can …