Dark Energy From Vacuum Fluctuations

The nature of the dark energy (DE) is one of the most outstanding problems of physical sciences today. Numerous and often ingenious attempts have been made to explain it, with multiple new papers appearing daily, yet no model proposed so far has gained a general acceptance. Modern approaches to the problem date from the pioneering papers by Zel’dovich [1], who was first to recognize the fundamental connection between the quantum physics and the macroscopically observable energy density of the vacuum, ρvac, manifested, e.g., as the cosmological constant. However, the simplest approaches using the Planck energy density lead to the well known problem of being off by some 123 orders of magnitude; and while many suggestions have been made as to how to solve this problem, none are yet compelling. Gurzadyan & Xue [2,3] (GX) proposed a model in which the energy density is contributed by the quantum fluctuations of the vacuum ground state, rather than the mean energy level itself. Whatever the value of the ground level is (including zero), if it is observed in a finite volume, e.g., within the particle horizon, it will be a subject to quantum fluctuations. Unless there is some as yet unknown limit to applicability of quantum mechanics (which would be a fundamental revelation by itself), such fluctuations are inevitable. Note that these are vacuum fluctuations, not particle fluctuations. This approach has been already hinted at by Zel’dovich [1]. Similar considerations have been also discussed recently by Padmanabhan [4,5]. Gurzadyan & Xue [2,3] derived a formula for the energy density contributed by the fluctuations, making reasonable assumptions of a simple topology, homogeneity and isotropy (so that only the radial modes matter). For example, the limits to the wavelengths of the vacuum modes can be given on the low end by the as-yet unknown characteristic length related to the quantum gravity (probably ~ the Planck length), and on the high end by the distance to the horizon. With reasonable estimates of these bounds, one gets values of the ρvac comparable to the observed value [2,3]. Here we expand on and refine their model, and compare it with observations. The GX formula can be written as: ρvac = (h/16c) (Lmin Lmax) = (πc/8G) (LPl /Lmin) 2 Lmax (1) where Lmin and Lmax are the lower and the upper bounds to the vacuum modes, and LPl =(Gh/2πc) To appear in Proc. UCLA Conference Dark Matter 2006, eds. D. Cline et al., Nuclear Pysics B, in press (2006)