Gravity of gluonic fluctuations and the value of the cosmological constant

Abstract

We analyze the classical linear gravitational effect of idealized pion-like dynamical systems, consisting of light quarks connected by attractive gluonic material with a stress–energy p = − ρ c 2 in one or more dimensions. In one orbit of a system of total mass M, quarks of mass m << M expand apart initially with v / c ∼ 1 , slow due to the gluonic attraction, reach a maximum size R 0 ∼ ℏ / M c , then recollapse. We solve the linearized Einstein equations and derive the effect on freely falling bodies for two systems: a gluonic bubble model where uniform gluonic stress–energy fills a spherical volume bounded by a 2D surface comprising the quarks’ rest mass, and a gluonic string model where a thin string connects two pointlike quarks. The bubble model is shown to produce a secular mean outward residual velocity of test particles that lie within its orbit. It is shown that the mean gravitational repulsion of bubble-like virtual-pion vacuum fluctuations agrees with the measured value of the cosmological constant, for a bubble with a radius equal to about twice the pion de Broglie length. These results support the view that the gravity of standard QCD vacuum fluctuations is the main source of cosmic acceleration.