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Relic Dark energy from Trans-Planckian Regime

Laura Mersini, Mar Bastero-Gil, Panagiota Kanti

Abstract

As yet, there is no underlying fundamental theory for the transplanckian regime. There is a need to address the issue of how the observables in our present universe are affected by processes that may have occured during the transplanckian regime. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta $k> M_P$. We name the range of the ultralow energy modes (of very short distances) that have frequencies equal or less than the current Hubble rate $H_0$ as the $\it{tail}$ 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 {\it dark energy} of the universe. During inflation, their energy is about 122-123 orders of magnitude smaller than the total energy. We present the exact solutions and show that: the CMBR spectrum is that of a (nearly) black body, and that the adiabatic vacuum is the only choice for the initial conditions. Finally, some of these results can also be applied to black hole physics.

Relic Dark energy from Trans-Planckian Regime

Abstract

As yet, there is no underlying fundamental theory for the transplanckian regime. There is a need to address the issue of how the observables in our present universe are affected by processes that may have occured during the transplanckian regime. A particular feature of the family of dispersion functions chosen is the production of ultralow frequencies at very high momenta . We name the range of the ultralow energy modes (of very short distances) that have frequencies equal or less than the current Hubble rate as the modes. These modes are still frozen today due to the expansion of the universe. We calculate their energy today and show that the provides a strong candidate for the {\it dark energy} of the universe. During inflation, their energy is about 122-123 orders of magnitude smaller than the total energy. We present the exact solutions and show that: the CMBR spectrum is that of a (nearly) black body, and that the adiabatic vacuum is the only choice for the initial conditions. Finally, some of these results can also be applied to black hole physics.

Paper Structure

This paper contains 5 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Set-Up and Formalism
  3. Exact Solution and the CMBR Spectrum
  4. Dark Energy from the "Tail"
  5. Conclusions

Figures (2)

  • Figure 1: Shown is our family of dispersion relations, for $\beta=1$ and representatives values of $\epsilon_1$ (solid lines). We have also included the Unruh's dispersion relation (dashed line) and the linear one (dotted line) for comparison.
  • Figure 2: The range of modes in the tail, $k_H < k < \infty$, defined by Eq. (\ref{['omegah']}). $H_0$ is the present value of the Hubble constant.