Cosmological Perturbation in f(T) Gravity Revisited
  We perform detailed investigation of cosmological perturbations in f(T)
theory of gravity coupled with scalar field. Our work emphasizes on the way to
gauge fix the theory and we examine all possible modes of perturbations up to
second order. The analysis includes pseudoscalar and pseudovector modes in
addition to the usual scalar, vector, and tensor modes. We find no
gravitational propagating degree of freedom in the scalar, pseudoscalar,
vector, as well as pseudovector modes. In addition, we find that the scalar and
tensor perturbations have exactly the same form as their counterparts in usual
general relativity with scalar field, except that the factor of reduced Planck
mass squared $M_{\text{pl}}^2 \equiv 1/(8\pi G)$ that occurs in the latter has
now been replaced by an effective time-dependentgravitational coupling $-2
(df/dT)|_{T=T_0}$, with $T_0$ being the background torsion scalar. The absence
of extra degrees of freedom of f(T) gravity at second order linear perturbation
indicates that f(T) gravity is highly nonlinear. Consequently one cannot
conclusively analyze stability of the theory without performing nonlinear
analysis that can reveal the propagation of the extra degrees of freedom.
