  Light bending due to strong gravity has recently been invoked to explain
variability and flux correlations between different bands in some accreting
black holes. A characteristic feature of light bending is reflection-dominated
spectra, especially if photon sources lie in the deepest parts of the
gravitational potential within a few gravitational radii of the event horizon.
We use the spectrum of the hard X-ray background in order to constrain the
prevalence of such reflection-dominated sources. We first emphasize the need
for reflection and explore the broad-band properties of realistic spectra that
incorporate light bending. We then use these spectra, in conjunction with the
observed 2-10 keV AGN distribution, evolutionary and obscuration functions in
order to predict the hard X-ray background spectrum over 3-100 keV, and provide
limits on the fraction of reflection-dominated objects, dependent on the height
of the photon sources. Our results allow for a cosmologically-significant
fraction of sources that incorporate strong light bending. The luminosity
function based on intrinsic flare luminosities is derived and implications
discussed. We discuss prospects for future hard X-ray missions such as NeXT and
Simbol-X that can image such sources as well as confirm the precise spectral
shape of the background near its peak, important for constraining the universal
relevance of light bending.
