A note on the 3D Brans-Dicke theory

TL;DR

This paper investigates the 3D Brans-Dicke theory's potential to describe dark matter and dark energy, analyzing its deceleration parameter and highlighting its limitations and possibilities in cosmological modeling.

Contribution

It explores the dimensional reduction of Brans-Dicke theory to three dimensions and evaluates its viability as a model for dark matter and dark energy.

Findings

Cannot model dark energy as k-essence

Can describe dark matter in 3D Brans-Dicke

Deceleration parameter analysis shows limitations

Abstract

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.