Keisuke Izumi, Yen Chin Ong
We performed detailed investigation into cosmological perturbation of f(T) theory of gravity coupled with scalar field. Our work emphasizes on the exact way of gauge fixing and we examined all possible modes of perturbations up to second order. This includes in addition to the usual scalar, vector, and tensor modes, also pseudoscalar and pseudovector modes; although we find that there is no gravitational propagating degrees of freedom in the scalar, pseudoscalar, vector, as well as pseudovector modes. We also 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relativity with scalar field, except that the factor of reduced Planck mass squared that occurs in the latter has now been replaced by an effective time-dependent gravitational coupling $-2 (df/dT)|_{T=T_0}$, with $T_0$ being the background torsion scalar.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, and one cannot conclusively analyze stability of the theory without performing nonlinear analysis that can reveal the propagation of the extra degrees of freedom.
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http://arxiv.org/abs/1212.5774
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