A Self-Gravitational Upper Bound on Localized Energy, Including that of Virtual Particles and Quantum Fields, which Yields a Passable "Dark Energy" Density Estimate

Abstract

The self-gravitational correction to a localized spherically-symmetric static energy distribution is obtained from energetically self-consistent upgraded Newtonian gravitational theory. The result is a gravitational redshift factor that is everywhere finite and positive, which both rules out gravitational horizons and implies that the self-gravitationally corrected static energy contained in a sphere of radius r is bounded by r times the fourth power of c divided by G. Even in the absence of spherical symmetry this energy bound still applies to within a factor of two, and it cuts off the mass deviation of any quantum virtual particle at about a Planck mass. Because quantum uncertainty makes the minimum possible energy of a quantum field infinite, such a field's self-gravitationally corrected energy attains the value of that field's containing radius r times the fourth power of c divided by G. Roughly estimating any quantum field's containing radius r as c times the age of the universe yields a "dark energy" density of 1.7 joules per cubic kilometer. But if r is put to the Planck length appropriate to the birth of the universe, that energy density becomes the enormous Planck unit value, which could conceivably drive primordial "inflation". The density of "dark energy" decreases as the universe expands, but more slowly than the density of ordinary matter decreases. Such evolution suggests that "dark energy" has inhomogeneities, which may be "dark matter".