A note on the 3D Brans-Dicke theory
  Since the evidence for an accelerated universe and the gap of 70% in the
total energy, collected by WMAP, search for alternatives for the general
relativity is an important issue, for this theory is not suited for these new
phenomena. A particular alternative is the Brans-Dicke theory which has being
allowing inspiring results, for example, concerning k-essence type fields in 4
dimensions. However, this theory is almost unexplored in the context of the
dimensional reduction of the theory in 3 dimensions. In this work, we address
some problems in this dimensional reduction, namely, evaluation of the
deceleration parameter of the universe described by the 3 dimensional
Brans-Dicke with and without matter. In both cases, we see that it is not
possible to consider the theory as a model of k-essence descrybing the dark
energy, but it can be considered as descrybing the dark matter.
