The Hubble relation for nonstandard candles and the origin of the redshift of quasars

It is shown that the magnitude-log (redshift) relation for brightest quasars can have a slope different from the value expected for standard candles. The value of this slope depends on the luminosity function and its evolution. Therefore the difference of this slope from the expected value cannot be used as evidence against the cosmological origin of the redshift of the quasars. It is shown that the observed variation of the luminosity of the brightest objects with redshift is consistent with the cosmological hypothesis and that it agrees with (and perhaps could be used to complement) the luminosity function obtained from V/Vm analysis. It is also shown that the nonzero slope of the magnitude-log (redshift) relation rules out the local quasar hypothesis, where it is assumed that the sources are nearby (less than 500 Mpc), that the bulk of their redshift is intrinsic, and that there is no dependence on distance of the intrinsic properties of the sources.