  The number of detected baryons in the Universe at z<0.5 is much smaller than
predicted by standard big bang nucleosynthesis and by the detailed observation
of the Lyman alpha forest at red-shift z=2. Hydrodynamical simulations indicate
that a large fraction of the baryons today is expected to be in a ``warm-hot''
(10^5-10^7K) filamentary gas, distributed in the intergalactic medium. This
gas, if it exists, should be observable only in the soft X-ray and UV bands.
Using the predictions of a particular hydrodynamic model, we simulated the
expected X-ray flux as a function of energy in the 0.1-2 keV band due to the
Warm-Hot Intergalactic Medium (WHIM), and compared it with the flux from local
and high red-shift diffuse components. Our results show that as much as 20% of
the total diffuse X-ray background (DXB) in the energy range 0.37-0.925keV
could be due to X-ray flux from the WHIM, 70% of which comes from filaments at
redshift z between 0.1 and 0.6. Simulations done using a FOV of 3', comparable
with that of Suzaku and Constellation-X, show that in more than 20% of the
observations we expect the WHIM flux to contribute to more than 20% of the DXB.
These simulations also show that in about 10% of all the observations a single
bright filament in the FOV accounts, alone, for more than 20% of the DXB flux.
Red-shifted oxygen lines should be clearly visible in these observations.
