Dilaton and modified gravity

We consider the dilaton in the strong string-coupling limit and elaborate on the original idea of Damour and Polyakov whereby the dilaton coupling to matter is minimized and vanishes at a finite value of the dilaton field. Combining this type of coupling with an exponential potential, the effective potential of the dilaton becomes matter density dependent. We study the background cosmology, showing that the dilaton can play the role of dark energy. We also analyze the constraints imposed by the absence of violation of the equivalence principle. Imposing these constraints and assuming that the dilaton plays the role of dark energy, we consider the consequences of the dilaton on large scale structures and, in particular, the behavior of the slip functions and the growth index at low redshift.