Cosmological evolution of brane world moduli

We study the cosmological consequences of nonconstant brane world moduli in five-dimensional brane world models with bulk scalars and two boundary branes. We focus on the case where the brane tension is an exponential function of the bulk scalar field, $U_b\propto \exp \left(\alpha \phi \right).\mathrm{}$ In the limit $\overrightarrow{\alpha }0,$ the model reduces to the two-brane model of Randall and Sundrum, whereas larger values of $\alpha$ allow for a less warped bulk geometry. Using the moduli space approximation we derive the four-dimensional low-energy effective action from a supergravity-inspired five-dimensional theory. For arbitrary values of $\alpha ,$ the resulting theory has the form of a biscalar-tensor theory. We show that, in order to be consistent with local gravitational observations, $\alpha$ has to be small (less than ${10}^{-2})$ and the separation of the branes must be large. We study the cosmological evolution of the interbrane distance and the bulk scalar field for different matter contents on each branes. Our findings indicate that attractor solutions exist which drive the moduli fields towards values consistent with observations. The efficiency of the attractor mechanism crucially depends on the matter content on each brane. In the five-dimensional description, the attractors correspond to the motion of the negative tension brane towards a bulk singularity, which signals the eventual breakdown of the four-dimensional description and the necessity of a better understanding of the bulk singularity.