We have studied the fluctuations of the soft ( 0.9–2 keV ) X–ray background intensity for \sim 10 arcmin and \sim 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 \Delta I _ { clus } are : ( \Delta I _ { clus } / I ) _ { 10 ~ { } arcmin } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt% \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } } 0.12 , ( \Delta I _ { clus } / I ) _ { 2 ~ { } arcmin } \mathrel { \hbox to 0.0 pt { \lower 3.0 pt% \hbox { $ \sim$ } \hss } \raise 2.0 pt \hbox { $ < $ } } 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 \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 ( \sim 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 \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 \sim 1 Mpc .