Hamiltonian formalism of the Jordan and Einstein frame representations of f(T) gravity

MARÍA JOSÉ GUZMÁN MONSALVE; RAFAEL FERRARO

Salamanca

Workshop; Teleparallel Universes in Salamanca; 2018

Modified teleparallel theories of gravity have attracted a lot of attention in the last years, due to its versatility to predict new physics both in high and low energy regimes. A source of intense debate lies on its Lorentz-breaking character and the nature of its degrees of freedom. The former aspect can be regarded as the theory selecting preferential tetrads that parallelize spacetime, or can be tackled by covariant versions of the theory. For the physical understanding of the degrees of freedom of this kind of theories, the Dirac-Bergmann algorithm for constrained Hamiltonian systems proves to be a powerful tool. Recent progress has been made on the Hamiltonian formulation of the teleparallel equivalent of general relativity and its simplest generalization, f(T) gravity. Our analysis shows that contrary to previous claims, f(T) gravity has only one extra degree of freedom for arbitrary dimension. This is revealed by the loss of one Lorentz generator, that pairs up with a constraint coming from the auxiliar scalar field (on the Jordan frame representation) to become second-class. To understand the counting of degrees of freedom, it will be helpful the comparison with the f(R) gravity case. As expected, the Hamiltonian formalism in f(T) gravity is frame dependent and could present limitations for some on-shell frames. Finally, we explore the feasibility of extending our formalism to the teleparallel Einstein frame and more general teleparallel-based theories of gravity.