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 $p=-\rho c^2$ in one or more dimensions. In one orbit of a system of total mass $M$, quarks of mass $m<<M$ expand apart initially with $v/c\sim 1$, slow due to the gluonic attraction, reach a maximum size $R_0 \sim \hbar/ Mc$, 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.