  The symmetry axes of active galactic nuclei (AGN) are randomly distributed in
space but highly inclined sources are heavily obscured and are not seen as
quasars with broad emission lines. The obscuring torus geometry determines the
average viewing angle, and if the torus geometry changes with the redshift,
this average viewing angle will also change. Thus the ratio between the
isotropic luminosity and observed luminosity may change systematically with
redshift. Therefore, if we use quasars to measure the luminosity distance by
evaluating the isotropic absolute luminosity and measuring the observed flux,
we can have a redshift-dependent bias which can propagate to cosmological
parameters. We propose a toy model for testing the effect of viewing angle
uncertainty on measurement of the luminosity distance. The model is based on
analytical description of the obscuring torus applied to one-parameter
observational data. It illustrates the possible change of the torus covering
factor between the two chosen redshift ranges. We have estimated the possible
error on specific cosmological parameters (H0,Omega_m) for the flat Lambda-CDM
cosmology if a method is calibrated at low redshift and applied to the higher
redshift. The errors on cosmological parameters due to potential dependence of
viewing angle on redshift are found to be potentially significant, and the
effect will have to be accommodated in the future in all quasar-based
cosmological methods. A careful systematic study of AGN mean viewing angle
across redshift is necessary, with the use of appropriate samples and models
which uniquely determine the inclination of each source.
