  We study the properties of the diffuse X-ray background by using the results
of a cosmological hydrodynamical simulation of the concordance LambdaCDM model.
The simulation follows gravitational and gas dynamics and includes a treatment
of physical processes like radiative cooling, star formation and supernova
feedback. From the simulation outputs, we produce a set of two-dimensional maps
of the intergalactic medium X-ray emission integrated over redshift. We find
that the signal in the soft (0.5-2 keV) band is lognormally distributed with a
mean intensity of about 4 10^-12 erg s^-1 cm^-2 deg^-2; approximately 40 per
cent of the emission originates from warm-hot gas (defined as baryons with
10^5<T<10^7 K), and 90 per cent comes from structures at z<0.9. Since the
spectrum is soft, being mostly provided by the intergalactic medium at low
temperature, the total mean intensity in the hard (2-10 keV) X-ray band is
smaller by a factor of about 4. In order to constrain the physical processes
included in our simulation, we compare our results with the observed upper
limit (1.2 +/- 0.3) 10^-12 erg s^-1 cm^-2 deg^-2 of the soft X-ray emission due
to diffuse gas. To this purpose, we remove the contributions of observable
extended objects (groups and clusters of galaxies) from the simulated maps by
adopting different detectability criteria which are calibrated on the
properties of systems at intermediate redshifts observed by Chandra. We show
that the simulated diffuse soft X-ray emission is consistent with the present
observed upper limit. However, if future measurements will decrease the level
of the unresolved X-ray background by a factor of two, a more efficient
feedback mechanism should be required to suppress the soft emission of the gas
residing within filaments and group-size haloes.
