Large "Dipolar" Vacuum Fluctuations in Quantum Gravity

Abstract

We study a novel set of gravitational field configurations, called "dipolar zero modes", which give an exactly null contribution to the Einstein action and are thus candidates to become large fluctuations in the quantized theory. They are generated by static unphysical sources satisfying (up to terms of order G^2) the simple condition Int d^3x T_00(x) = 0. We give two explicit examples of virtual sources: (i) a "mass dipole" consisting of two separated mass distributions with different signs; (ii) two concentric "+/- shells". The field fluctuations can be large even at macroscopic scale. There are some, for instance, which last ~ 1 s or more and correspond to the field generated by a virtual source with size ~ 1 cm and mass ~ 10^6 g. This appears paradoxical, for several reasons, both theoretical and phenomenological. We also give an estimate of possible suppression effects following the addition to the pure Einstein action of cosmological or R^2 terms.