Quantum Gravity will be studied in the context of early universe cosmology. Specifically, inhomogeneous perturbations, and their evolution, within Loop Quantum Cosmology will be developed so as to allow direct observational testing of the theory. A phase of the early universe that is dominated by Quantum Gravity may produce effects observable in the detailed structure of the Cosmic Microwave Background or large scale galaxy distributions. In order to understand and quantify such effects the power spectra and non-gaussianities of scalar and tensor perturbations, will be calculated within Loop Quantum Cosmology. This will then allow the theory to be directly tested against a wide range of observational data, such that from the WMAP and Plank satellites and various deep field galaxy surveys. This would provide us with a unique window into the deep Quantum Gravity regime and an unprecedented probe of ultra high energy physics.This project will require a significant extension of the Loop Quantum Cosmological model which should follow as closely as possible the full underlying Loop Quantum Gravity theory. Thus this project will simultaneously strengthen the link between Loop Quantum Cosmology and the full theory whilst also producing (potentially) observable predictions. Since quantum field theory in curved space-times is a key part of cosmological perturbation theory, this project will also draw links between full Loop Quantum Gravity, quantum fields on a semi-classical space-time and classical cosmology.Although the main thrust of this project will be aimed towards Loop Quantum Cosmology, the methods developed will be applicable to other approaches to Quantum Gravity. This project will provide a toolbox with which many theories of Quantum Gravity can, for the first time, be tested and constrained against observations. This if particularly timely due to the flood of precision cosmological data that will come from the next generation of observatories.