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Gauge Theories for gravitation: foundations and cosmological applications


The teleparallel equivalent of general relativity, which corresponds to a gauge theory for the translation group, is nowadays considered to be a viable alternative theory for gravitation. Due to its gauge structure, it has shown to be more appropriate than general relativity to study some specific problems of gravitation. Considering this context, the basic purpose of this project is to study further the theoretical foundations of teleparallel gravity, as well as to apply this model to study some specific questions which has not found consistent answers in the usual context of general relativity. In particular, the following items will be of interest: 1. To develop a Hamiltonian formulation for teleparallel gravity. Then, we plan to apply the technics of Loop Quantum Gravity (LQG) in an attempt to obtain a quantum theory for gravitation. The main motivation of this topic concerns the natural affinity of the LQT theory with the gauge theories, which makes of teleparallel gravity a more appropriate theory than general relativity to study quantum gravity. 2. To study the duality symmetry of gravitation. 3. To explore the consequences of the local Lorentz invariance of teleparallel gravity for a possible definition of a covariant energy density for gravitation. 4. To re-analize the theory of the gravitational waves from the teleparallel point of view. 5. To explore deeper the relation between the cosmological term and the conformal symmetry. 6. To explore the cosmological consequences of a dynamical cosmological term. (AU)

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