Weinberg's theorem, phantom crossing and screening

We consider models where the dilaton, seen as the pseudo-Goldstone boson of broken scale invariance, plays the role of dark energy. We revisit Weinberg's theorem and show that quantum corrections induced by the graviton lead to the screening of the dilaton locally. We also discuss the time evolution of the equation of state and find that phantom crossing is a natural feature of these models. The time variation of the equation of state and its deviation from $-1$ is limited by screening locally and can only be relaxed when the dilaton is allowed to have a mass of the order of the Hubble rate cosmologically, thus going beyond single-field screened dark-energy models. This obstruction extends to all single-field screened models of the chameleon-type where the large mass of the scalar on cosmological scales leads to a negligible variation of the equation of state at low redshift.