The Gleyzes-Langlois-Piazza-Vernizzi ( GLPV ) theories up to quartic order are the general scheme of scalar-tensor theories allowing the possibility for realizing the tensor propagation speed c _ { t } equivalent to 1 on the isotropic cosmological background .
We propose a dark energy model in which the late-time cosmic acceleration occurs by a simple k-essence Lagrangian analogous to the ghost condensate with cubic and quartic Galileons in the framework of GLPV theories .
We show that a wide variety of the variation of the dark energy equation of state w _ { DE } including the entry to the region w _ { DE } < -1 can be realized without violating conditions for the absence of ghosts and Laplacian instabilities .
The approach to the tracker equation of state w _ { DE } = -2 during the matter era , which is disfavored by observational data , can be avoided by the existence of a quadratic k-essence Lagrangian X ^ { 2 } .
We study the evolution of nonrelativistic matter perturbations for the model c _ { t } ^ { 2 } = 1 and show that the two quantities \mu and \Sigma , which are related to the Newtonian and weak lensing gravitational potentials respectively , are practically equivalent to each other , such that \mu \simeq \Sigma > 1 .
For the case in which the deviation of w _ { DE } from -1 is significant at a later cosmological epoch , the values of \mu and \Sigma tend to be larger at low redshifts .
We also find that our dark energy model can be consistent with the bounds on the deviation parameter \alpha _ { H } from Horndeski theories arising from the modification of gravitational law inside massive objects .