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Modified Brans-Dicke Theory in Arbitrary Dimensions

Within an algebraic framework, used to construct the induced-matter-theory (IMT) setting, in $(D+1)$-dimensional Brans-Dicke (BD) scenario, we obtain a modified BD theory (MBDT) in $D$ dimensions. Being more specific, from the $(D+1)$-dimensional field equations, a $D$--dimensional BD theory, bearing new features, is extracted by means of a suitable dimensional reduction onto a hypersurface orthogonal to the extra dimension. In particular, the BD scalar field in such $D$-dimensional theory has a self-interacting potential, which can be suitably interpreted as produced by the extra dimension. Subsequently, as an application to cosmology, we consider an extended spatially flat FLRW geometry in a $(D+1)$-dimensional space-time. After obtaining the power-law solutions in the bulk, we proceed to construct the corresponding physics, by means of the induced MBDT procedure, on the $D$-dimensional hypersurface. We then contrast the resulted solutions (for different phases of the universe) with those usually extracted from the conventional GR and BD theories in view of current ranges for cosmological parameters. We show that the induced perfect fluid background and the induced scalar potential can be employed, within some limits, for describing different epochs of the universe. Finally, we comment on the observational viability of such a model.