The Soft X-Ray Background as a Calorimeter: Filament Emission Bounds Thermalised Vacuum Energy

If any of the vacuum's energy has been thermalised into the warm-hot intergalactic medium, the gas must eventually radiate it, and the sky's diffuse soft X-ray background is where the receipts accumulate. This paper turns the background into a calorimeter for filament gas. A representative filament (overdensity 15, electron density 3.30e-06 per cubic centimetre, 30 Mpc effective emitting path) is assigned a thermalised vacuum fraction phi, so that its energy density is phi times the surviving vacuum density u_L = 5.25e-09 erg per cubic centimetre, fixing its temperature and its band emissivity in the 0.5-2 keV window where the diffuse background is measured at about 4e-13 erg per second per square centimetre per steradian. Requiring the filament network not to outshine that background bounds phi at 2.97e-09 — at which the gas temperature is only 8.98e03 K, far below the million-degree warm-hot regime. The thermalised fraction that would actually hold filament gas at 1e6 K (3.31e-07) overproduces the background by a factor of 346; at 3e6 K (9.93e-07) the overproduction is 739; at 1e7 K it is 896. The soft X-ray background therefore certifies that the thermalised share of the surviving vacuum density in cosmic filaments is below three parts in a billion — a factor of nine tighter than the warm-hot medium's own heat content allows — and that no part of the warm-hot medium's million-degree temperatures is paid for by thermalised vacuum energy at anywhere near the required level. Computed from stated assumptions; not a measurement.