The evolution of a diffuse baryonic medium in a flat Friedmann univers
e containing cold or hybrid (cold plus hot) dark matters has been stud
ied in the linear regime. This approximation is reasonable if one cons
iders only the features of the intergalactic medium (IGM) on large sca
les where the details of energy and mass exchanges between the diffuse
medium and lumpy objects (quasars and galaxies) are less important. O
ne can then avoid a direct description of the interaction, but approxi
mate the medium as a polytropic gas. Numerical and analytical calculat
ions showed that for all models considered, the spectrum of density fl
uctuations of the IGM can be expressed on average as a proportion of t
hose of dark matters by a factor less than 1, in which the only parame
ter is the Jeans length of the medium. This solution can provide a coh
erent explanation of cosmological properties of the IGM, including the
cosmic Mach number of IGM, Comptonization (Zel'dovich-Sunyaev) parame
ter, and soft X-ray emission of the IGM. This model showed that the IG
M temperature underwent an increase with cosmic time. It implies that
(1) clusters may have a halo consisting of hot and thin diffuse baryon
ic medium, and (2) the temperature of the X-ray gas of clusters increa
ses with the distance from the center of the cluster. The X-ray temper
ature profiles of Perscus and Virgo Clusters recently given by ROSAT r
ecently appears to consist with these results. The model can also be t
ested in the following ways: (1) the Comptonization parameter y may no
t be lower than 10(-4); (2) the IGM X-ray emission may not be larger t
han that of cosmic X-ray background by a faction of 20% at 0.1 keV and
15% at the 0.3 keV band.