Loop Quantum Cosmology: Relation Between Theory and Observations

This chapter provides a review of the frameworks developed for cosmological perturbation theory in loop quantum cosmology and applications to various models of the early universe including inflation, ekpyrosis, and the matter bounce, with an emphasis on potential observational consequences. It also includes a discussion on extensions to include non-Gaussianities and background anisotropies, as well as on its limitations concerning trans-Planckian perturbations and quantization ambiguities. It concludes with a summary of recent work studying the relation between loop quantum cosmology and full loop quantum gravity.