Trans-Planckian dark energy?

It has recently been proposed by Bastero-Gil, Mersini and co-workers that dark energy could be attributed to the cosmological properties of a scalar field with a nonstandard dispersion relation that decreases exponentially at wave numbers larger than the Planck scale ${(k}_{\mathrm{phys}}>M_{\mathrm{Pl}}).\mathrm{}$ In this scenario, the energy density stored in the modes of trans-Planckian wave numbers but sub-Hubble frequencies produced by amplification of the vacuum quantum fluctuations would account naturally for the dark energy. The present paper examines this model in detail and shows step by step that it does not work. In particular, we show that this model cannot make definite predictions since there is no well-defined vacuum state in the region of wave numbers considered: hence, the initial data cannot be specified unambiguously. We also show that for most choices of initial data this scenario implies the production of a large amount of energy density (of order $\sim M_{\mathrm{Pl}}^4)$ for modes with momenta $\sim M_{\mathrm{Pl}},$ far in excess of the background energy density. We evaluate the amount of fine tuning in the initial data necessary to avoid this back-reaction problem and find it is of order ${H/M}_{\mathrm{Pl}}.$ We also argue that the equation of state of the trans-Planckian modes is not vacuumlike. Therefore this model does not provide a suitable explanation for the dark energy.