Soft X-ray background fluctuations and large-scale structure in the Universe

We have studied the fluctuations of the soft (0.9-2 keV) X-ray background intensity for ~10 arcmin and ~2 arcmin beam sizes, using 80 high galactic latitude medium-deep images from the ROSAT position sensitive proportional counter (PSPC). These fluctuations are dominated (and well reproduced) by confusion noise produced by sources unresolved with the beam sizes we used. We find no evidence for any excess fluctuations which could be attributed to source clustering. The 95 per cent confidence upper limits on excess fluctuations dIclus are: dIclus/Ixrb_10 arcmin<~ 0.12, dIclus/Ixrb_2 arcmin <~0.07. We have checked the possibility that low surface brightness extended objects (like groups or clusters of galaxies) may have a significant contribution to excess fluctuations, finding that they are not necessary to fit the distribution of fluctuations, and obtaining an upper limit on the surface density for this type of source. Standard Cold Dark Matter models would produce dIclus/Ixrb larger than the above limits for any value of the density of the Universe Omega=0.1-1, unless the bias parameter of the X-ray emitting matter is smaller than unity, or an important fraction of the sources of the soft X-ray background (~30 per cent) is at redshifts z>1. Limits on the 2-10 keV excess fluctuations are also considered, showing that X-ray sources in that band have to be at redshifts z>1 unless Omega>0.4. Finally, if the spatial correlation function of the sources that produce these excess fluctuations is instead a power law, the density contrast drho/rho implied by the excess fluctuations reveals that the Universe is smooth and linear on scales of tens of Mpc, while it can be highly non-linear on scales ~1 Mpc.