Extra Dimensions, Dilaton and Dark Energy

Abstract: In view of the recent observations showing that the universe is accelerating we discuss dilaton and radion stabilization from a phenomenological perspective using perfect fluid sources. One general conclusion we present is that the pressure coefficient along extra dimensions should be -2 if that of the observed dimensions is -1, the latter mimicking a cosmological constant compatible with experimental data. The conditions on the dilaton coupling are similarly strong: we find that if the coupling of the dilaton $\phi$ to fields other than gravity is of the form $\sqrt{-g}\;e^{(a-2)\phi}\;\mathcal{L}$ where $\mathcal{L}$ representing all other fields yielding the mentioned fluid, $a$ must be -2 if space-time dimensionality is 10. Within our approach these conditions result taking constant radion and dilaton at the level of the equations of motion. To ameliorate this we also discuss how dynamical stabilization may be achieved with a simple variant in which a dilaton potential is added in the picture where the mentioned constraints are shown to remain.