Relic dark energy from the trans-Planckian regime - art. no. 043508

As yet, there is no underlying fundamental theory for the trans-Planckian r egime. There is a need to address the issue of how the observables in our p resent Universe are affected by processes that may have occurred at super-P lanckian energies (referred to as the trans-Planckian regime). Specifically , we focus on the impact the trans-Planckian regime has on two observables: namely, dark energy and the cosmic microwave background radiation (CMBR) s pectrum. We model the trans-Planckian regime by introducing a I-parameter f amily of smooth non-linear dispersion relations which modify the frequencie s at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high mo menta k (for k>M-p). We name the range of the ultralow energy modes (of ver y short distances) that have frequencies equal to or less than the current Hubble rate Ho as the tail modes. These modes are still frozen today due to the expansion of the Universe. We calculate their energy today and show th at the tail provides a strong candidate for the dark energy of the Universe . During inflation, their energy is about 122 to 123 orders of magnitude sm aller than the total energy, for any random value of the free parameter in the family of dispersion relations. For this family of dispersions, we pres ent the exact solutions and show that the CMBR spectrum is that of a (nearl y) blackbody, and that the adiabatic vacuum is the only choice for the init ial conditions.