Abstract
In the context of f(R,T) theories of gravity, we study the evolution of scalar cosmological perturbations in the metric formalism. According to restrictions on the background evolution, a specific model within these theories is assumed in order to guarantee the standard continuity equation. Using a completely general procedure, we find the complete set of differential equations for the matter density perturbations. In the case of sub-Hubble modes, the density contrast evolution reduces to a second-order equation. We show that for well-motivated f(R,T) Lagrangians the quasistatic approximation yields to very different results from the ones derived in the frame of the concordance {\Lambda}CDM model constraining severely the viability of such theories.
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