  We explore the intergalactic medium (IGM) as a potential source of the
unresolved soft X-ray background (XRB) and the feasibility to extract the IGM
state and evolution from XRB observations. We build two analytical models, the
continuum field model and the halo model, to calculate the IGM XRB mean flux,
angular auto correlation and cross correlation with galaxies. Our results
suggest that the IGM may contribute a significant fraction to the unresolved
soft XRB flux and correlations. We calibrated non-Gaussian errors estimated
against our $512^3$ moving mesh hydro simulation and estimate that the ROSAT
all sky survey plus Sloan galaxy photometric redshift survey would allow a
$\sim 10%$ accuracy in the IGM XRB-galaxy cross correlation power spectrum
measurement for $800<l<5000$ and a $\sim 20%$ accuracy in the redshift resolved
X-ray emissivity-galaxy cross correlation power spectrum measurement for
$z\lesssim 0.5$. At small scales, non-gravitational heating, e.g. feedback,
dominates over gravity and leaves unique signatures in the IGM XRB, which
allows a comparable accuracy in the measurement of the amount of
non-gravitational heating and the length scales where non-gravitational energy
balances gravity.
