Modified dispersion relations from closed strings in toroidal cosmology

Abstract

A long-standing problem of theoretical physics is the exceptionally small value of the cosmological constant ⌳ϳ10 Ϫ120 measured in natural Planckian units. Here we suggest how this tiny number might arise from a toroidal string cosmology based on closed strings. In this picture the dark energy would arise from a correlation between momentum and winding modes that for short distances has an exponential fall-off with increasing values of the momenta. The freeze-out by the expansion of the background universe for these trans-Planckian modes might be interpreted as a frozen condensate of the closed-string modes in the three noncompactified spatial dimensions. Our qualitative arguments are heuristic in nature and published only because they may suggest an improved treatment of the connection between strings and cosmological expansion.

Trans-Planckian dark energy?

“…[1,2,3], the dispersion relation departs from its standard linear form and approach a decreasing exponential at large wave-numbers. This type of dispersion relation could possibly emerge from string theory [2].…”

“…[1,2,3], the dispersion relation departs from its standard linear form and approach a decreasing exponential at large wave-numbers. This type of dispersion relation could possibly emerge from string theory [2]. It has been argued that the energy density of the modes of sub-Planckian wavelengths and sub-Hubble frequencies (referred to as "tail" modes) is naturally of the same order as the critical energy density today and has the same equation of state as a cosmological constant.…”

“…Recently, it has been claimed in a series of articles [1,2,3] that the cosmic dark energy component could be explained naturally by the trans-Planckian energy of a scalar field with a suitable non-linear dispersion relation in the trans-Planckian regime. Such dispersion relations, which relate the frequency ω phys to the wave-number k phys of a scalar field wave-packet, and which depart from the standard linear dispersion relation in the trans-Planckian regime are a way of modeling phenomenologically the unknown physics for sub-Planckian wavelengths.…”

“…[1,2,3] that the dark energy could be attributed to the cosmological properties of a scalar field with a non-standard dispersion relation that decreases exponentially at wave-numbers larger than Planck scale (k phys > M Pl ). 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.…”

Equation of state of the trans-Planckian dark energy and the coincidence problem

“…This model is based on the nonlinear behavior of transplanckian metric perturbation modes which was motivated by closed string theory [3,4] and quantum gravity [5]. The transplanckian dark energy (TDE) model was based on the freeze-out mechanism of the short-distance modes with ultralow energy, by the expansion of the background universe, H, and it naturally explained the smallness of the observed dark energy.…”