The X-ray background as a probe of density fluctuations at high redshift

The X-ray background (XRB) probes structure on scales intermediate between those explored by local galaxy redshift surveys and by the COBE microwave background measurements. We predict the large-scale angular fluctuations in the XRB, expressed in terms of spherical harmonics for a range of assumed power spectra and evolution scenarios. The dipole is a result of large-scale structure as well as a result of the observer's motion (the Compton-Getting effect). For a typical observer the two effects turn out to be comparable in amplitude. The coupling of the two effects makes it difficult to use the XRB for independent confirmation of the CMB dipole being a result of the observer's motion. The large-scale structure dipole (rms per component) relative to the monopole is in the range a(1m)/a(00) similar to (0.4-9.0) x 10(-3). The spread is mainly because of the assumed redshift evolution scenarios of the X-ray volume emissivity rho(x)(z). The prediction of the dipole is consistent with a measured dipole in the HEA01 XRB map. Typically, the harmonic spectrum drops with l like a(lm) similar to l(-0.4). This behaviour allows us to discriminate a true clustering signal against the flux shot noise, which is constant with I, and may dominate the signal unless bright resolved sources are removed from the XRB map. We also show that Sachs-Wolfe and Doppler (as a result of the motion of the sources) effects in the XRB are negligible. Although our analysis focuses on the XRB, the formalism is general and can be easily applied to other cosmological backgrounds.