Relic dark energy from the trans-Planckian regime

Abstract

As yet, there is no underlying fundamental theory for the trans-Planckian regime. There is a need to address the issue of how the observables in our present Universe are affected by processes that may have occurred at super-Planckian energies ͑referred to as the trans-Planckian regime͒. Specifically, we focus on the impact the trans-Planckian regime has on two observables: namely, dark energy and the cosmic microwave background radiation ͑CMBR͒ spectrum. We model the trans-Planckian regime by introducing a 1-parameter family of smooth non-linear dispersion relations which modify the frequencies at very short distances. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta k ͑for kϾM P ). We name the range of the ultralow energy modes ͑of very short distances͒ that have frequencies equal to or less than the current Hubble rate H 0 as the tail modes. These modes are still frozen today due to the expansion of the Universe. We calculate their energy today and show that 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 smaller than the total energy, for any random value of the free parameter in the family of dispersion relations. For this family of dispersions, we present the exact solutions and show that the CMBR spectrum is that of a ͑nearly͒ blackbody, and that the adiabatic vacuum is the only choice for the initial conditions.

Dynamics of chaotic inflation with variable space dimension

“…[2,4], we do not rule out the case for which the space dimension at the Planck length to be equal to 10. For this case, the radius of the Universe at the onset of inflation is smaller than the Planck length, and one may consider the inflationary cosmology with the variable space dimension in the trans-Planckian problem, which is a currently active research [10][11][12][13][14][15][16][17][18][19][20][21][22]. We will address in detail this problem in [7].…”

“…In such a research, length scales of order the current horizon size could very easily have started out during inflation smaller than the Planck length, with no inconsistency from the standpoint of classical physics [10][11][12][13][14][15][16][17][18][19][20][21][22]. Based on the issue of the trans-Planckian problem some arguments in the paper [2] no longer apply, particularly the constraints from requiring the initial radius of curvature to be larger than the Planck length l P .…”

Generalized Lorentz invariance with an invariant energy scale

“…Such modified dispersion relations also may lead to corrections to the predictions of inflationary cosmology, observable in future high precision measurements of the CMB spectrum [11]. Finally a modified dispersion relation may lead to an explanation of the dark energy, in terms of energy trapped very high momentum and low-energy quanta, as pointed out by Mersini and collaborators [12].…”

Cosmological perturbations from a new-physics hypersurface

“…It has been argued, for instance, that in the de Sitter case corrections in the two-point function of the metric fluctuations are linear in the ratio H/Λ [7], computable, and possibly observable [10] (see also [11,12,13] for different perspectives). While some aspects of this suggestion may be theoretically justified according to our previous discussion, the mere existence of a cut-off does not allow, in our opinion, to compute accurately any specific correction to observables unless the nature of the physics above the cut-off is, even roughly, specified.…”