On the emergence of the \(\mathbf{\Lambda }\) CDM model from self-interacting Brans–Dicke theory in \(\mathbf{d= 5}\)

We investigate whether a self-interacting Brans–Dicke theory in \(d=5\) without matter and with a time-dependent metric can describe, after dimensional reduction to \(d=4\), the FLRW model with accelerated expansion and non-relativistic matter. By rewriting the effective 4-dimensional theory as an autonomous 3-dimensional dynamical system and studying its critical points, we show that the \(\varLambda \)CDM cosmology cannot emerge from such a model. This result suggests that a richer structure in \(d=5\) may be needed to obtain the accelerated expansion as well as the matter content of the 4-dimensional universe.