Effect of a varying gravitational constant on the SN Ia Hubble diagram,AGN luminosity evolution,and X-ray source counts

The impact of a cosmic time evolution of the gravitational constant on SN Ia luminosity and AGN/QSO luminosity functions is studied. The gravitational constant scales linearly with the Hubble parameter, its present-day variation being \(\dot{G}_{0}/G_{0}\approx 1.9\times 10^{-4}\)?Gyr^?1, compatible with current bounds from lunar laser ranging. Distance moduli of Type Ia supernovae are fitted with a cosmic expansion factor derived from temperature variations of planetary paleoclimates, and a luminosity dependence on look-back time proportional to the varying gravitational constant is inferred from the Hubble diagram. A fit is performed to the comoving space density of X-ray-selected active galactic nuclei (AGNs) and optically selected quasars (QSOs) extending to redshifts z≈6. The initial steep increase of the AGN space density is reproduced by a redshift evolution depending solely on the Hubble parameter as scaling variable. The AGN luminosity scales with the Hubble parameter, and the scaling exponents of the luminosity function, composed of two competing power laws with exponential cutoff, are obtained. Based on the AGN luminosity function, flux-limited X-ray source counts are investigated. The counting functions are derived and put to test by fitting cumulative number counts of soft X-ray point sources compiled from ROSAT, XMM-Newton, and Chandra surveys.