Towards scaling cosmological solutions with full coupled Horndeski Lagrangian: the KGB model

Abstract

We study a general scalar field Lagrangian coupled with matter andlinear in □ϕ (also called KGB model). Within this class ofmodels, we find the most general form of the Lagrangian that allowsfor cosmological scaling solutions, i.e. solutions where the ratioof matter to field density and the equation of state remain constant.Scaling solutions of this kind may help solving the coincidence problemsince in this case the presently observed ratio of matter to darkenergy does not depend on initial conditions, but rather on the theoreticalparameters. Extending previous results we find that it is impossibleto join in a single solution a matter era and the scaling attractor.This is an additional step towards finding the most general scalingLagrangian within the Horndeski class, i.e. general scalar-tensormodels with second order equations of motion.