3 Possibilities of a QED - Based Vacuum Energy

A QED-based bootstrap mechanism, appearing at sufficiently small space-time scales, is suggested as an explanation for the " dark " vacuum energy that may be able to accelerate the universe. Very-small-scale virtual vacuum currents are assumed to generate small-scale electromagnetic fields, corresponding to the appearance of an effective 4-potential A ext µ (x), which is itself equal to the vev of the operator A µ (x) in the presence of that A ext µ (x). The latter condition generates a bootstrap-like equation for A ext µ (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 10 8 GeV if all three lepton bubbles are included. Virtual quark bubbles are not expected to be important, except for the possibility of providing the initial " spark " which sets off the QED bootstrap. A multiplicative 4-vector v µ , whose magnitude is determined by a comparison with the average mass density needed to produce the observed acceleration is introduced, and may characterize 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 1 from 10 −5 cm (corresponding to a " spontaneous QED-vacuum phase change ") to 10 −13 cm (representing a " polarization of the QED vacuum " by quark-antiquark pairs of the QCD vacuum). Treated as a constant, or " averaged " 4-vector in these estimates, v µ is understood to have a non-perturbative QED or QCD origin. Near the light-cone, such vacuum electric fields become large, suggesting the possibility of copious lepton-pair production, resulting in a " plasma " which tends to diminish the fields. This suggests a non-perturbative change in the definition of the QED vacuum, which can act to provide a convergence factor for all QED perturbative calculations ; in essence, the parameter M defines the scale at which all high-momentum Feynman graphs converge. Four questions are proposed which carry this non-perturbative, vacuum-field mechanism towards unexpected consequences, involving the possible production of tachy-onic lepton-pairs that contribute to " dark " or " missing " matter, while acting as a source of galactic gamma-ray bursts and ultra-high-energy cosmic rays.