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We explore the intergalactic medium (IGM) as a potential source of theunresolved soft X-ray background (XRB) and the feasibility to extract the IGMstate and evolution from XRB observations. We build two analytical models, thecontinuum field model and the halo model, to calculate the IGM XRB mean flux,angular auto correlation and cross correlation with galaxies. Our resultssuggest that the IGM may contribute a significant fraction to the unresolvedsoft XRB flux and correlations. We calibrated non-Gaussian errors estimatedagainst our $512^3$ moving mesh hydro simulation and estimate that the ROSATall sky survey plus Sloan galaxy photometric redshift survey would allow a$\sim 10%$ accuracy in the IGM XRB-galaxy cross correlation power spectrummeasurement for $800<l<5000$ and a $\sim 20%$ accuracy in the redshift resolvedX-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, whichallows a comparable accuracy in the measurement of the amount ofnon-gravitational heating and the length scales where non-gravitational energybalances gravity.Comment: 17 pages, 5 figures. Will appear on ApJ May issu

Measuring Feedback Using the Intergalactic Medium State and Evolution Inferred from the Soft X‐Ray Background