The growth of matter perturbations in some scalar–tensor DE models

Abstract

We consider asymptotically stable scalar–tensor dark energy (DE) models for which the equation of stateparameter wDE tends to zero in the past. The viable models are of the phantom type today: however, thisphantomness is milder than in general relativity if we take into account the varyinggravitational constant when dealing with the SNIa data. We study further the growth ofmatter perturbations and we find a scaling behaviour on large redshifts which couldprovide an important constraint. In particular, the growth of matter perturbations on largeredshifts in our scalar–tensor models is close to the standard behaviour , while it is substantially different for the best-fit model in general relativity for the sameparametrization of the background expansion. As for the growth of matter perturbations onsmall redshifts, we show that in these models the parameter can take absolute values much larger than in models inside general relativity. Assuming a constantγ when γ′0 is large would lead to a poor fit of the growth functionf. This provides another characteristic discriminative signature for these models.