The soft X-ray background and galaxy clusters

We show that the background flux observed in X-rays around 1 keV sets a tight upper limit to the evolution of X-ray-emitting clusters of galaxies, once the contribution of the sources now resolved is subtracted. Specifically, if the clustering proceeds up a scale-invariant hierarchy in a critical universe, the intracluster gas content must increase faster than the dynamical mass. We model such evolution in terms of infall of the intergalactic medium into the hierarchically growing potential wells, limited by the intergalactic temperature. Thus the soft X-ray background provides constraints to the dynamical clustering and to the history of the intergalactic medium, which extend those being provided by the z-resolved luminosity functions in X-rays and complement those expected from measuring the Comptonization parameter in the microwave and far-IR bands.