Dark energy and matter perturbations in scalar-tensor theories of gravity

We solve analytically and numerically the generalized Einstein equations in scalar tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the. corresponding results for minimally coupled quintessence perturbations. We find that Scalar-Tensor dark energy density perturbations are amplified by a factor of about 10(4) compared to minimally coupled quintessence perturbations on scales less than about 1000h(-1)Mpc (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about-10% compared to matter density perturbations. Scalar-Tensor dark energy density perturbations are anti-correlated with matter linear perturbations on sub Hubble scales. This anti-correlation of matter with negative pressure perturbations induces a mild amplification of natter perturbations by about 10% on sub-Hubble scales. The. evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound (C-s Phi = 0). We briefly discuss the observational implications of our results which may include predictions for galaxy and cluster halo profiles which are modified compared to ACDM. The observed properties of these profiles are known to be in some tension with the predictions of ACDM.