  In this work we present a model of dark matter based on scalar-tensor theory
of gravity. With this scalar field dark matter model we study the non-linear
evolution of the large scale structures in the universe. The equations that
govern the evolution of the scale factor of the universe are derived together
with the appropriate Newtonian equations to follow the non-linear evolution of
the structures. Results are given in terms of the power spectrum that gives
quantitative information on the large-scale structure formation. The initial
conditions we have used are consistent with the so called concordance
$\Lambda$CDM model.
