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.
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