A Kaluza-Klein Inspired Brans-Dicke Gravity with Dark Matter and Dark Energy Model

We propose the Kaluza-Klein inspired Brans-Dicke gravity model containing possible existence of dark matter and dark energy. The massive scalar field coupled with gravity in 5 dimensional spacetime can be reduced to 4 dimensional gravity along with the dilaton $\phi$, gauge fields $A_{\mu}$, and the tower of scalar fields $\eta_n$. Two additional gauge fields are introduced to form "Cosmic Triad" vector field scenario. We then use the dynamical system approach to analyze the critical points and their corresponding physical parameters. We found that in the case where only the zero mode of the Kaluza-Klein scalar is decoupled, the system contains both dark matter and dark energy phase depending on the mass parameter with the presence of the gauge field.