Cosmological constraints on hot plasma in a closed universe

A hot uniform collisionally heated intergalactic medium (IGM) at closure density is reconsidered. During the recombination epoch only the observational data of the soft X-ray region and the optical depths of H Ly..cap alpha.. need be used to ascertain the viability of such a dense cosmic H and He plasma. The results indicate a present temperature in the range 1.6 x 10/sup 5/< or approx. =T/sub 0/< or approx. =4.2 x 10/sup 6/ K if the reheating of the IGM ceased at z/sup h//sub off/approx.3, the latest possible time. As cessation of heating moves to earlier times, the range of T/sub 0/ allowed narrows until at the earliest possible z/sup h//sub off/approx.12 only T/sub 0/approx.1.6 x 10/sup 5/ K is acceptable. Relevant formulae are provided to modify these numbers as new data becomes available. Ths IGM avoids any hard X-ray production and thus assumes that discrete sources alone constitute the entire cosmic X-ray background.