The precision of intensity measurements of the extragalactic X-ray Background ( XRB ) on an angular scale of about a degree is dominated by spatial fluctuations caused by source confusion noise .
X-ray source counts at the flux level responsible for these fluctuations , \sim 10 ^ { -12 } { erg } { cm } ^ { -2 } { s } ^ { -1 } , will soon be accurately measured by new missions and it will then be possible to detect the weaker fluctuations caused by the clustering of the fainter , more distant sources which produce the bulk of the XRB .
We show here that measurements of these excess fluctuations at the level of \left ( { \Delta I \over I } \right ) \sim 2 \times 10 ^ { -3 } are within reach , improving by an order of magnitude on present upper limits .
Since it is likely that most ( if not all ) of the XRB will be resolved into sources by AXAF , subsequent optical identification of these sources will reveal the X-ray volume emissivity in the Universe as a function of redshift .
With these ingredients , all-sky observations of the XRB can be used to measure the power spectrum of the density fluctuations in the Universe at comoving wavevectors k _ { c } \sim 0.01 - 0.1 { Mpc } ^ { -1 } at redshifts where most of the XRB is likely to originate ( z \sim 1 - 2 ) with a sensitivity similar to , or better than , the predictions from large-scale structure theories .
A relatively simple X-ray experiment , carried out by a large-area proportional counter with a 0.5 - 2 \deg ^ { 2 } collimated field-of-view scanning the whole sky a few times , would be able to determine the power spectrum of the density fluctuations near its expected peak in wavevector with an accuracy better than 10 per cent .