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of reduced Planck mass squared M _ { \text { pl } } ^ { 2 } \equiv 1 / ( 8 \pi G ) that occurs in the latter has now been replaced by an effective time-dependent gravitational coupling -2 ( df / dT ) | _ { T = T _ { 0 } } , with T _ { 0 } being the background torsion scalar .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 can not conclusively analyze stability of the theory without performing nonlinear analysis that can reveal the propagation of the extra degrees of freedom .