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We propose the rest-frame 2-10 keV photon index, \ga, acting as an indicatorof the bolometric correction, \lb/$L_{\rm 2-10keV}$ (where \lb~ is thebolometric luminosity and $L_{\rm 2-10keV}$ is the rest-frame 2-10 keVluminosity), in radio-quiet active galactic nuclei (AGNs). Correlations between\ga~ and both bolometric correction and Eddington ratio are presented, based onsimultaneous X-ray, UV, and optical observations of reverberation -mapped AGNs.These correlations can be compared with those for high-redshift AGNs to checkfor any evolutionary effect. Assuming no evolutionary effect in AGNs' spectralproperties, together with the independent estimates of $L_{\rm 2-10keV}$, thebolometric correction, Eddington ratio, and black hole (BH) mass can all beestimated from these correlations for high-redshift AGNs, with the meanuncertainty of a factor of 2-3. If there are independent estimates of BHmasses, \ga~ for high-redshift AGNs can be used to determine their true \lb~and $L_{\rm 2-10keV}$, and in conjunction with the redshift, can be potentiallyused to place constraints on cosmology by comparison with the rest-frame 2-10keV flux. We find that the true $L_{\rm 2-10keV}$ estimated from \ga~ for thebrightest Type I AGNs with $z<1$ in the Lockman Hole is generally in agreementwith the observed $L_{\rm 2-10keV}$.  However, there are still many uncertainties, such as the accuratedetermination of the intrinsic \ga~ for distant AGNs and the large uncertaintyin the luminosities obtained, which call for significant further study before``AGN cosmology'' can be considered a viable technique.

Hard X-ray photon index as an indicator of bolometric correction in active galactic nuclei