Several popular cosmological models predict that a large fraction of the baryonic mass in the local Universe is located in filamentary and sheet-like structures associated with galaxy overdensities. This gas is expected to be gravitationally heated to temperatures of about one million degrees, therefore emitting in the soft X-rays. By analysing wide field soft-X ray images we have obtained some of the very first evidences of diffuse X-ray emission associated with galaxy overdensities (Zappacosta, Maiolino et al. 2005a, Zappacosta, Mannucci, Maiolino et al. 2002, Zappacosta, Maiolino et al. 2005b). The most likely interpretation of such diffuse soft X-ray emission is that it is tracing Warm-Hot Intergalactic Medium associated with the overdensity of galaxies.

Additional evidence for Warm-Hot Intergalactic Medium was obtained through X-ray spectroscopy of quasars in the background of large scale structures traced by galaxy overdensities, which have revealed absorption features associated with highly ionized species (O VII) at the same redshift of the large scale structure (Fang et al. 2010, Zappacosta, Nicastro, Maiolino et al. 2010).