The k-essence scalar field in the context of Supernova Ia observations

We study a framework where the hypothesis of a minimum length in space-time is complemented with the notion of reference frame invariance. It turns out natural to interpret the action of the obtained reference frame transformations in the context of doubly special relativity. As a consequence of this formalism we find interesting connections between the minimum length properties and the modified velocity-energy relation for ultra-relativistic particles. For example, we can predict the ratio between the minimum lengths in space and time using the results from OPERA on superluminal neutrinos.