  In the context of scalar-tensor theories we study the evolution of the
density contrast for Jordan-Fierz-Brans-Dicke theories in a
Friedmann-Lemaitre-Robertson-Walker Universe. Calculations are performed in the
Einstein Frame with the cosmological background described as Lambda-Cold Dark
Matter (Lambda-CDM) and supplemented by a Jordan-Fierz-Brans-Dicke field. By
using a completely general procedure valid for all scalar-tensor theories, we
obtain the exact fourth-order differential equation for the density contrast
evolution in modes of arbitrary size. In the case of sub-Hubble modes, the
expression reduces to a simpler but still fourth-order equation that is then
compared with the standard (quasistatic) approximation. Differences with
respect to the evolution as predicted by the standard Concordance Lambda-CDM
model are observed depending on the value of the coupling.
