Hamiltonian analysis of covariant teleparallel gravity

Abstract: The conventional action formulation for general relativity is by the Einstein-Hilbert action, which depends on the Levi-Civita connection and the metric. However, a classically equivalent theory can be done by formulating the action in terms of torsion (related to the antisymmetric part of the affine connection) and tetrads. This is done in the theory called teleperallel equivalent to general relativity. From this formulation as a starting point it is not evident from a quick look that this theory should be selected in favor of other modified teleparallel theories of gravity. This gives a motivation from a fundamental point of view to investigate the theory further, where the Hamiltonian analysis is useful since it can give insights of the canonical structure of a theory.

In the literature there is some work on the Hamiltonian analysis for the most basic teleparallel theories of gravity. However, they are either incomplete, contradicting to other work, not formulated in a covariant way, or a combination of these. In this talk I will outline the derivation of the so-called primary Hamiltonian for the most basic covariant teleparallel theories of gravity. I explicitly write out these Hamiltonians without putting the so-called spin connection to zero. Then, I will briefly talk about perturbations in the aforementioned theories and use this to show that they are most likely not viable theories. The irreducible decomposition of the torsion scalar will be discussed in order to reach some insights on the fundamental relevance for the irreducible components and their relation to propagating fields. If time allows I will spend some time on discussing future directions where a teleparallel bigravity construction might avoid theoretical pathologies while providing an interesting theory of gravity.

astrophysicscondensed mattergeneral relativity and quantum cosmologyhigh energy physicsmathematical physicsclassical physicsgeneral physics

Audience: researchers in the topic

Theoretical physics seminar @ Tartu