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 active galactic nucleus 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 New X-ray Telescope/Non-thermal Energy eXploration Telescope and Simbol-X that can image such sources as well as confirm the precise spectral shape of the X-ray background near its peak, important for constraining the universal relevance of light bending.
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