  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.
