Towards a QED-Based Vacuum Energy

Abstract

A QED-based mechanism, breaking translational invariance of the vacuum at sufficiently small distance scales, is suggested as an explanation for the vacuum energy pressure that accelerates the universe. Very-small-scale virtual vacuum currents are assumed to generate small-scale electromagnetic fields corresponding to the appearance of a 4-potential $A_{\mu}^{ext} (x)$, which is itself equal to the vev of the operator $ A_{\mu}(x)$ in the presence of that $A_{\mu}^{ext}(x)$. The latter condition generates a bootstrap-like equation for $A_{\mu}^{ext}(x)$ which has an approximate, tachyonic-like solution corresponding to propagation outside the light cone, and damping inside; this solution is given in terms of a mass parameter M that turns out to be on the order of the Planck mass if only the simplest, electron vacuum-bubble is included; if the muon and tau bubbles are included, M decreases to $\sim 10^6 - 10^7$ GeV. A multiplicative 4-vector $v_{\mu}$, whose magnitude is determined by a comparison with the average mass density needed to produce the observed acceleration is introduced, and characterizes the distance d over which the fields so produced may be expected to be coherent; the present analysis suggests that d can lie anywhere in the range from $10^{-5} cm$ (corresponding to a "spontaneous vacuum phase change") to $10^{-13}cm$ (representing a "polarization of the QED vacuum" by quark-antiquark pairs of the QCD vacuum). Near the light-cone, such electric fields become large, introducing the possibility of copious charged-particle pair production, whose back-reaction-fields tend to diminish the vacuum electric field. The possibility of an experimental test of the resulting plasma at large momentum transfers is discussed.