Equation of state of the trans-Planckian dark energy and the coincidence problem

Observational evidence suggests that our Universe is presently dominated by a dark energy component and is undergoing accelerated expansion. We recently introduced a model, motivated by string theory for short-distance physics, for explaining dark energy without appealing to any fine tuning. The idea of trans-Planckian dark energy (TDE) was based on the freeze-out mechanism of the ultralow frequency modes, $\omega \mathrm{}\left(k\right),$ of very short distances, by the expansion of the background universe, $\omega \mathrm{}\left(k\right)\mathrm{}<~H.\mathrm{}$ In this paper we address the issue of the stress-energy tensor for nonlinear short-distance physics and explain the need to modify Einstein equations in this regime. From the modified Einstein equations we then derive the equation of state for the TDE model, which has the distinctive feature of being continually time dependent. The explanation of the coincidence puzzle relies entirely on the intrinsic time evolution of the TDE equation of state.