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 backgro und intensity for similar to 10 and similar to 2 arcmin beam sizes, us ing 80 high galactic latitude medium-deep images from the ROSAT positi on sensitive proportional counter (PSPC). These fluctuations are domin ated (and well reproduced) by confusion noise produced by sources unre solved with the beam sizes we used. We find no evidence for any excess fluctuations which could be attributed to source clustering. The 95 p er cent confidence upper limits on excess fluctuations Delta I-clus ar e: (Delta I-clus/I)(10arcmin)less than or similar to 0.12, (Delta I-cl us/I)(2arcmin)less than or similar to 0.07. We have checked the possib ility that low surface brightness extended objects (like groups or clu sters of galaxies) may have a significant contribution to excess fluct uations, finding that they are not necessary to fit the distribution o f fluctuations, and obtaining an upper limit on the surface density fo r this type of source. Standard cold dark matter models would produce Delta I/I 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 (similar to 30 per cent) is at r edshifts z > 1. Limits on the 2-10 keV excess fluctuations are also co nsidered, showing that X-ray sources in that band have to be at redshi fts z > 1 unless Omega > 0.4. Finally, if the spatial correlation func tion of the sources that produce these excess fluctuations is instead a power law, the density contrast delta rho/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 of similar to 1 Mpc.