Perturbations and stability conditions of k-essence and kinetic gravity braiding models in two-field measure theory

We study cosmological perturbations for k-essence and kinetic gravity braiding models in the context of the two-field measure theory (TMT). Considering scalar perturbations and the uniform field gauge, we obtain the sound speed of the fields and present a stability analysis by means of the kinetic matrix and the mass eigenvalues. For k-essence models, in the two-field measure theory, the speed of propagation of the field is modified completely due to the new measure field and it gives rise to crucial differences with respect to the case without new measure. The stability analysis gives a physical viable model for the Universe. For the kinetic gravity braiding models in the two-field measure theory we get that, in general, the speed of perturbations is equal to the speed of light which is a consequence of the properties of the new measure field. In the later case, there is always a ghost field. Furthermore, we calculate general expressions for the mass eigenvalues and find, for an explicit example, the existence of tachyonic instabilities.