K-essential covariant holography

The holographic principle is applied to a flat Friedmann-Robertson-Walker space-time dominated by dark energy when this is due to the presence of a k-essence scalar field, both for dark energy and phantom scenarios. In this framework, a geometrical covariant approach permits the construction of holographic hypersurfaces. The resulting covariant preferred screens, both for phantom and non-phantom regions, are then compared with those obtained by using the holographic dark energy model with the future event horizon as the infrared cut-off. In the phantom case, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analysed whether this covariant formalism allows a mathematically consistent formulation of fundamental theories based on the existence of a S-matrix at infinite distances.