Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the LCDM solution of general relativity at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard LCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in LCDM and the f(R) model both in the complete and quasi\hs static regimes.