Large scale structure and matter power spectrum in f ( T ) gravity

In the present manuscript the scalar linear perturbations and matter power spectrum are investigated in the context of f(T) gravity using both dynamical system and 1 + 3 covariant approaches. After introducing the background gravitational field equations in the context of f(T) gravity, we obtain autonomous differential equations using dynamical system analysis. We then define covariant perturbation variables and use scalar decomposition, harmonic and redshift transformation techniques to obtain the energy density contrast in redshift space. After solving the obtained energy density contrast equations in quasi-static approximation, we compute matter power spectrum in the context of f(T) gravity. The importance of studying linear scalar perturbations for the defined f(T) model and the relevance of different initial conditions in computing the matter power spectrum are also stressed. It is reported that matter power spectrum for f(T) gravity, for a particular functional form of f(T) model considered is not scale invariant as the case for General Relativity.