Pseudoinvariance and the extra degree of freedom in f(T) gravity

Understand

Nonlinear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudoinvariant under local Lorentz transformations of the tetrad field.

• This procedure consequently leads to the loss of the local pseudoinvariance and the appearance of additional degrees of freedom (d.o.f.).
• The constraint structure of f(T) gravity suggests the existence of one extra d.o.f.
• when compared with GR, which should describe some aspect of the orientation of the tetrad.