EPRL/FK asymptotics and the flatness problem - Camoes de Oliveira, Jose Ricardo (2016)
The main topic of this thesis is a key point in testing the viability of the EPRL/FK spin foam model as a quantum theory of gravity. While it is common knowledge that there are fundamental mathematical inconsistencies between Einstein's General Relativity and Quantum Mechanics, pointing, among other reasons, towards the necessity of such a theory, our current inability to observe the extremely high energies and/or small wavelengths at which quantum effects are expected to appear leaves us with mathematical consistency tests as the only, albeit incomplete, way of separating possibly viable models from incorrect ones. One of the most basic tests available is the study of the model's asymptotics in a semiclassical regime. Indeed, any quantum theory of gravity must be able to reproduce Einstein's model when quantum effects are negligible. With that in mind, we will discuss the asymptotics of spin foam models, in particular the EPRL/FK prescription, and note the non-trivial issues that arise in the course of that study.