Degrees of freedom and problems in f(T) gravity

Torsion-based modified theories of gravity, such as f(T) gravity, are arguably one of the very few "true" modified gravities based on well-defined geometric structures. However, the original formulation explicitly works in a specific choice of frame, which has led to considerable amount of confusion in the literature about these theories breaking local Lorentz invariance. Pathological properties such as superluminal propagation and the lack of well-posedness of Cauchy problem were found to plague f(T) gravity. Recent effort to " covariantize"f(T) gravity has, however, renewed interests in this subject. In this proceeding paper, we review and discuss issues concerning the actual number of degrees of freedom in f(T) gravity, and how this might relate to the aforementioned pathologies.