DBI Galileons in the Einstein frame: Local gravity and cosmology

It is shown that a disformally coupled theory in which the gravitational sector has the Einstein-Hilbert form is equivalent to a quartic Dirac-Born-Infeld Galileon Lagrangian, possessing nonlinear higher derivative interactions, and hence allowing for the Vainshtein effect. This Einstein frame description considerably simplifies the dynamical equations and highlights the role of the different terms. The study of highly dense, nonrelativistic environments within this description unravels the existence of a disformal screening mechanism, while the study of static vacuum configurations reveals the existence of a Vainshtein radius, at which the asymptotic solution breaks down. Disformal couplings to matter also allow the construction of dark energy models, which behave differently than conformally coupled ones and introduce new effects on the growth of large scale structure over cosmological scales, on which the scalar force is not screened. We consider a simple disformally coupled dark matter model in detail, in which standard model particles follow geodesics of the gravitational metric and only dark matter is affected by the disformal scalar field. This particular model is not compatible with observations in the linearly perturbed regime. Nonetheless, disformally coupled theories offer enough freedom to construct realistic cosmological scenarios, which can be distinguished from the standard model through characteristic signatures.