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 backgroundintensity for ~10 arcmin and ~2 arcmin beam sizes, using 80 high galacticlatitude medium-deep images from the ROSAT position sensitive proportionalcounter (PSPC). These fluctuations are dominated (and well reproduced) byconfusion noise produced by sources unresolved with the beam sizes we used. Wefind no evidence for any excess fluctuations which could be attributed tosource clustering. The 95 per cent confidence upper limits on excessfluctuations dIclus are: dIclus/Ixrb_10 arcmin<~ 0.12, dIclus/Ixrb_2 arcmin<~0.07. We have checked the possibility that low surface brightness extendedobjects (like groups or clusters of galaxies) may have a significantcontribution to excess fluctuations, finding that they are not necessary to fitthe distribution of fluctuations, and obtaining an upper limit on the surfacedensity for this type of source. Standard Cold Dark Matter models would producedIclus/Ixrb larger than the above limits for any value of the density of theUniverse Omega=0.1-1, unless the bias parameter of the X-ray emitting matter issmaller than unity, or an important fraction of the sources of the soft X-raybackground (~30 per cent) is at redshifts z>1. Limits on the 2-10 keV excessfluctuations are also considered, showing that X-ray sources in that band haveto be at redshifts z>1 unless Omega>0.4. Finally, if the spatial correlationfunction of the sources that produce these excess fluctuations is instead apower law, the density contrast drho/rho implied by the excess fluctuationsreveals that the Universe is smooth and linear on scales of tens of Mpc, whileit can be highly non-linear on scales ~1 Mpc.Comment: 10 pages, LaTeX file, epsf.sty and 7 postscript figures. To appear in MNRAS. Fig. 7 replaced, some references improved, a few corrections to the tex