Consistency of the pulsating universe with Einstein’s field equations

Abstract

It is shown that the pulsating model of the universe can be derived from Einstein’s field equations with the addition of a traceless, negative-energy source tensor. Bounds on the negative-energy density are given. Earlier works on negative-energy sources as well as prevention of singularities are discussed. The results support earlier findings that one can obtain a bounce without modifying Einstein’s field equations, but instead, by violating the Hawking-Penrose strong energy condition. The negative-energy tensor is interpreted as the partially uncompensated zero-point energy of a weakly interacting, neutral massless fermion (which may or may not be a massless neutrino). It is shown explicitly that the zero-point quadratic divergences, reported earlier by Ford for the photon and the massless fermion, do not cancel, in contrast to the quartic divergences. To eliminate both the quadratic as well as the quartic divergences, three auxiliary massless fermions and six conformai scalars are introduced. The resulting multiplet is analogous to that of a massless multiplet forN = 4 supersymmetry with comparable helicity states. The corresponding small Casimir energy is evaluated. Since the model predicts a cosmic background of weakly interacting negative-energy radiation, greater in intensity than the CMB radiation, it can be experimentally falsified. A subordinate idea of the model, that there was an astrophysical- rather than a Planckian-size bounce, can be falsified by suitable computer simulations.