Zero-point energy and continuous creation of matter in an expanding universe

Abstract

A purely Kinematic model of universe is considered that is described a priori by, (i) the Robertson-Walker space-time metric, (ii) the classical conservation law for energy-mass, and (iii) the observational fact of uniform Hubble expansion. It is shown that continuous creation of matter takes place in such a universe as a direct consequence of a secular quantum effect, provided that the physical vacuum is treated as the ground state of a certain quantized field obeying Bose statistics. Under the adiabatic hypothesis, the zero-point energy content per unit proper volume of the physical vacuum decreases parametrically (i.e. as a function of a time-dependent cut-off parameter) due to the cosmological red-shift, concomitant with the Hubble expansion. This secular zero-point energy defect reappears necessarily as an accession of observable energy-mass (so as to satisfy the conservation law) and may be expected to compensate for the material rarefaction due to the universal expansion. The observable energy-mass density ρ(t) at any epoch t, normalized with respect to its value ρ(0) at the epoch t = 0, is given by a simple equation ξ_η(t) =ρ(t)/ρ(0) = (1+η)e^-3Ht-ηe^-4Ht, where η is an adjustable parameter (dimensionless) and H the Hubble constant. Based on certain heuristic reckonings, the age T₀ of the universe is shown to be given by T₀ = H^-1 ln (4/3), which is remarkably enough independent of η.