Dynamical systems analysis of the cubic galileon beyond the exponential potential and the cosmological analogue of the vDVZ discontinuity

In this paper we generalize the dynamical systems analysis of the cubic galileon model previously investigated in De Arcia et al (2016 Class. Quantum Grav. 33 125036) by including self-interaction potentials beyond the exponential one. It will be shown that, consistently with the results of De Arcia et al (2016 Class. Quantum Grav. 33 125036), the cubic self-interaction of the galileon vacuum appreciably modifies the late-time cosmic dynamics by the existence of a phantom-like attractor (among other super-accelerated solutions that do not modify in any appreciable way the late-time dynamics and hence are not of interest in the present investigation). In contrast, in the presence of background matter the late-time cosmic dynamics remains practically the same as in the standard quintessence scenario. This means that we can not recover the cubic galileon vacuum continuously from the more general cubic quintessence with background matter, by setting to zero the matter energy density (and the pressure). This happens to be a kind of cosmological vDVZ discontinuity that can be evaded by means of the cosmological version of the Vainshtein screening mechanism.