  Extensive measurements of the X-ray background (XRB) yield a reasonably
reliable characterisation of its basic properties. Having resolved most of the
cosmic XRB into discrete sources, the levels and spectral shapes of its main
components can be used to probe both the source populations and also
alternative cosmological and large-scale structure models. Recent observations
of clusters seem to provide evidence that clusters formed earlier and are more
abundant than predicted in the standard $\Lambda$CDM model. This motivates
interest in alternative models that predict enhanced power on cluster scales.
We calculate predicted levels and spectra of the superposed emission from
groups and clusters of galaxies in $\Lambda$CDM and in two viable alternative
non-Gaussian ($\chi^2$) and early dark energy models. The predicted levels of
the contribution of clusters to the XRB in the non-Gaussian models exceed the
measured level at low energies and levels of the residual XRB in the 2-8 keV
band; these particular models are essentially ruled out. Our work demonstrates
the diagnostic value of the integrated X-ray emission from clusters, by
considering also its dependences on different metallicities, gas and
temperature profiles, Galactic absorption, merger scenarios, and on a
non-thermal pressure component. We also show that the XRB can be used for a
upper limit for the concentration parameter value.
