A phenomenological approach to quintessence in scalar-tensor gravity
  This talk is based on my work in collaboration with B. Boisseau, D. Polarski, and A.A. Starobinsky. The most natural and best-motivated alternatives to general relativity are the so-called "scalar-tensor" theories, in which the gravitational interaction is mediated not only by a (spin-2) graviton, but also by a (spin-0) scalar field. We study quintessence in this general framework, and show that the microscopic Lagrangian of the theory can be unambiguously reconstructed from two observable cosmological functions of the redshift: the luminosity distance and the linear density perturbation of dustlike matter. We also analyze the constraints imposed on the theory by the knowledge of only the first of these functions, as it will probably be available sooner with a good accuracy. [The main interest of this very short paper is to give the equations in the "Brans-Dicke" parametrization.] 
G. Esposito-Farese