On the emergence of the ${\bf\Lambda}$CDM model from self-interacting Brans-Dicke theory in ${\bf d= 5}$

TL;DR

This paper examines whether a 5D self-interacting Brans-Dicke theory can produce a 4D universe with accelerated expansion and matter, concluding that it cannot directly lead to the $f ext{Lambda}$CDM model.

Contribution

It demonstrates that the $f ext{Lambda}$CDM cosmology does not emerge from a simple 5D self-interacting Brans-Dicke framework after dimensional reduction.

Findings

$f ext{Lambda}$CDM does not arise from the model.

A richer 5D structure may be necessary.

The effective 4D theory cannot reproduce accelerated expansion.

Abstract

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 three-dimensional dynamical system and studying its critical points, we show that the $\Lambda$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.