H II Region Expansion Bounds Any Local Enhancement of the Surviving Vacuum Density

If the surviving vacuum density were locally enhanced — concentrated by a factor xi above its cosmic mean in the neighbourhood of galaxies — its repulsive active density (rho + 3P/c^2 = -2 xi rho_L) would push outward on ionised gas, and the expansion of H II regions is a clock against which such a push can be timed. This paper integrates the standard pressure-driven expansion of an H II region (ionising photon rate 1e49 per second into gas at 1e3 per cubic centimetre; Strömgren radius 0.68 pc) with the vacuum acceleration added, and finds the enhancement at which the radius at fixed age departs by ten percent from the unperturbed solution. The region reaches 1.42 pc at 1e5 years, 2.37 pc at 3e5 years and 4.50 pc at 1e6 years unperturbed. A ten-percent radius excess requires xi = 8.89e09 at 1e5 years, 1.15e09 at 3e5 years, and 1.14e08 at 1e6 years; at the cosmic value xi = 1 the fractional effect is of order 1e-10 or smaller. Because observed H II regions match the standard expansion ages and sizes without any anomalous outward term, local enhancements of the vacuum density in star-forming environments are bounded at xi below roughly 1e08 to 1e09 — a weak bound in absolute terms, and the honest one for this probe, but fully independent of the fragmentation bound from molecular clouds. Computed from stated assumptions; not a measurement.