Quantum gravity – as defined in the Feynman path integral approach by a gravitational action and a functional measure over metrics – is in principle a unique theory. While additional higher derivative terms that are consistent with general covariance are in principle allowed in the action, they affect only the physics at very short distances. As shown by Feynman, the Einstein-Hilbert action plus a cosmological constant term represents the unique covariantly-quantized theory for a massless spin-two particle at large distances – much like the Yang-Mills theory and QED are for massless spin-one particles. While the theory is still infamously perturbatively nonrenormalizable, a wide range of modern analytical and numerical methods have been developed in the past decades to study precisely such theories. From the nonlinear Heisenberg magnet in three dimensions to QCD in four dimensions (in the nonperturbative limit), these methods have produced many useful predictions with remarkable accuracies. Furthermore, important new physics have been revealed with these nonperturbative methods – such as the existence of quantum condensates, anomalous dimensions in critical scaling exponents, and nontrivial phase transitions – that would otherwise be invisible with perturbation theory to any order.
In this dissertation, we explore the consequences of these techniques applied to gravity. Using a range of analytical to numerical methods, we derive a number of physical predictions to the gravitational effects on cosmology. In particular, we explore the unique alternative explanation for the various cosmological power spectra (including the galaxy- and CMB-spectra) that is based on gravitational fluctuations, as derived using various nonperturbative quantum field-theoretical methods. This is contrasted with the currently popular inflationary models, which are based on fluctuations of scalar fields. Next, we also outline a number of testable predictions in this picture that deviate from the conventional picture of inflation. The key ingredients in this new picture are the appearance of a nontrivial gravitational vacuum condensate (directly related to the observed cosmological constant), and a calculable renormalization group running of Newton's $G$ on cosmological scales. Finally, we compare these results to latest available cosmological observational data, and we find that the results fit very well with the majority of the data. However, the limited precision of the observational data on largest angular scales, which is where the deviations are most significant, does not yet allow us to clearly prove or disprove either set of ideas. Nevertheless, it is expected that with an influx of increasingly accurate observational data in the near future, the new quantum gravitational picture we presented here can be subjected to further stringent observational tests, thus helping us gain a deeper understanding of roles that quantum field theory and gravity play in our Universe.
