The Vacuum Term in the Jeans Criterion: A Computed Non-Effect and the Enhancement It Would Require

In general relativity the quantity that sources local gravitational acceleration is the active density rho + 3P/c^2, which for the vacuum component equals -2 rho_L: a repulsive contribution that formally belongs in the Jeans criterion for self-gravitating gas, replacing the gas density by rho_gas - 2 rho_L. This paper computes the size of that correction across the molecular-cloud regime and converts it into a bound on any local enhancement of the vacuum density. For a cloud at 10 K and hydrogen density 1e4 per cubic centimetre, the Jeans length is 0.212 pc and the Jeans mass 2.87 solar masses; including the vacuum term at its cosmic value shifts the Jeans mass by a fraction 4.50e-10. At the diffuse end of the cloud regime (1e2 per cubic centimetre, Jeans mass 28.7 solar masses) the shift is 4.50e-08. To move the Jeans mass by one percent at 1e4 per cubic centimetre, the local vacuum density would have to exceed its cosmic value by a factor xi = 2.20e07; to move it by fifty percent, xi = 7.90e08. Star formation's basic scales are therefore independent of the vacuum sector at any enhancement below millions — a clean non-effect, stated with its margin, which also serves as the reference bound for any model in which the surviving vacuum density is locally concentrated. Computed from stated assumptions; not a measurement.