A note on trans-Planckian tail effects

We study the proposal by Mersini et al. [1] that the observed dark energy might be explained by the back-reaction of the set of tail modes in a theory with a dispersion relation in which the mode frequency decays exponentially in the trans-Planckian regime. The matter tail modes are frozen out, however they induce metric fluctuations. The energy-momentum tensor with which the tail modes effect the background geometry obtains contributions from both metric and matter fluctuations. We calculate the equation of state induced by the tail modes taking into account the gravitational contribution. We find that, in contrast to the case of frozen super-Hubble cosmological fluctuations, in this case the matter perturbations dominate, and they yield an equation of state which to leading order takes the form of a positive cosmological constant.