MEASURING THE POWER SPECTRUM OF DENSITY-FLUCTUATIONS AT INTERMEDIATE REDSHIFT WITH X-RAY-BACKGROUND OBSERVATIONS

The precision of intensity measurements of the extragalactic X-ray bac kground (XRB) on an angular scale of about a degree is dominated by sp atial fluctuations caused by source confusion noise. X-ray source coun ts at the flux level responsible for these fluctuations, similar to 10 (-12) erg cm(-2) s(-1), will soon be accurately measured by new missio ns, and it will then be possible to detect the weaker fluctuations cau sed by the clustering of the fainter, more distant sources which produ ce the bulk of the XRB. We show here that measurements of these excess fluctuations at the level of (Delta I/I) similar to 2 x 10(-3) are wi thin 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 resolve d into sources by AXAF, subsequent optical identification of these sou rces will reveal the X-ray volume emissivity in the Universe as a func tion of redshift. With these ingredients, all-sky observations of the XRB can be used to measure the power spectrum (PS) of the density fluc tuations in the Universe at comoving wavevectors k(c) similar to 0.01- 0.1 Mpc(-1) at redshifts where most of the XRB is likely to originate (z similar to 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 PS of the density fluctuations n ear its expected peak in wavevector with an accuracy better than 10 pe r cent.