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 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, ~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 (DeltaI/I)~2x10^-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 (PS) of the density fluctuations in the Universe at comoving wavevectors k_c~0.01-0.1 Mpc^-1 at redshifts where most of the XRB is likely to originate (z~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 near its expected peak in wavevector with an accuracy better than 10 per cent.