Quantum fields and gravity: Expanding space-times

We discuss a proposal for a somewhat new formulation of quantum field theory (set in a four-dimensional manifold, the space-time) that includes an analysis of its implications for the evolution of Einstein-Friedmann cosmological models. The proposed theory displays two peculiar features: (i) a local Hilbert-Fock space is associated with each spacetime point: we are dealing with a vector bundle whose fibers are Hilbert spaces; the operator-valued sections of the bundle are the quantum fields; (ii) the vacuum energy density is finite, being regularized in a space-time curvature dependent way, independently at each point. In fact everything is finite: self-masses, self-charges, quantum fluctuations: they depend on the space-time curvature and diverge only for a flat metric. In an Einstein-Friedmann model the vacuum (zero-point) energy density is consequently time-dependent and in general not negligible. Then it is shown that, for some choices of the parameters of the theory, the big-bang singularity is resolved and replaced by a bounce driven by the vacuum energy density, which becomes (very) large and negative near the bounce (negative by the contribution of the Fermi fields). But for large times (now, say) the Bose fields' positive vacuum energy eventually overcomes the negative one and we are finally left with the present vacuum energy: positive and reasonably small.