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

Abstract

Abstract We investigate whether a self-interacting Brans–Dicke theory in $$d=5$$ d=5 without matter and with a time-dependent metric can describe, after dimensional reduction to $$d=4$$ 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 $$\varLambda $$ Λ CDM cosmology cannot emerge from such a model. This result suggests that a richer structure in $$d=5$$ d=5 may be needed to obtain the accelerated expansion as well as the matter content of the 4-dimensional universe.