LOOP QUANTUM COSMOLOGY (LQC)
LQC deals with the canonical quantization of symmetry reduced models for general relativity, cosmological models for instance, adapting the techniques of loop quantum gravity to the reduced model under consideration. The main goal of this approach is to get a resolution of the classical singularities at the quantum level, by means of the quantum corrections coming from the geometry. This quantization program has been developed quite successfully in the case of homogeneous models. My main interest in this field of research is the extension of the LQC program to inhomogeneous models (midisuperspaces), such as Gowdy cosmologies.
Spinfoams, the covariant framework for loop quantum gravity, attempt to provide a discrete (and regularized) path integral formalism for quantum gravity. They provide transition amplitudes between quantum states of geometry (spin-network states). Spinfoam cosmology deals with the investigation of simple spinfoam configurations, as an attempt to model with them symmetry reduced models for general relativity, such as cosmological models. At this respect, I am not only interested in the possibility of actually being able to model cosmology using the spinfoam dynamics, but also in using these simple spinfoam configurations to understand the link between the covariant and the canonical dynamics.
COARSE-GRAINING OF TOY SPINFOAM MODELS
In order to confirm whether spinfoam models really provide a theory for quantum gravity, it is essential to investigate their continuum limit and check that it is in agreement with general relativity. One way to do this is to analyze their renormalization flow under coarse-graining. This task is highly complicated, mainly due to the fact that spinfam models for quantum gravity are based on Lie groups. As a starting point to go in this direction, one can define toy models based on finite groups still capturing, up to some extend, most of the main features of the full spinfoam models. These models provide a manageable arena to analyze the phase transition from the discrete to the continuum.