Quasars accreting matter at very high rates (known as extreme Population A [xA] quasars, possibly associated with super-Eddington accreting massive black holes) may provide a new class of distance indicators covering cosmic epochs from present day up to less than 1 Gyr from the Big Bang. At a more fundamental level, xA quasars are of special interest in studies of the physics of AGNs and host galaxy evolution. However, their observational properties are largely unknown. xA quasars can be identified in relatively large numbers from major optical surveys over a broad range of redshifts, thanks to selection criteria defined from the systematic changes along the quasars main sequence. It has been possible to build a sample of about 250 quasars at low and intermediate redshift, and larger samples can be easily selected from the latest data releases of the Sloan Digital Sky Survey. A large sample can clarify the main properties of xA quasars which are expected - unlike the general population of quasars - to radiate at an extreme, well defined Eddington ratio with small scatter. As a result of the small scatter in Eddington ratio shown by xA quasars, we propose a method to derive the main cosmological parameters based on redshift-independent "virial luminosity" estimates from measurements of emission line widths, roughly equivalent to the luminosity estimates based from line width in early and late type galaxies. A major issue related to the cosmological application of the xA quasar luminosity estimates from line widths is the identification of proper emission lines whose broadening is predominantly virial over a wide range of redshift and luminosity. We report on preliminary developments using the AlIII 1860 intermediate ionization line and the Hydrogen Balmer line H-beta as virial broadening estimators, and we briefly discuss the perspective of the method based on xA quasars.

21 pages, 3 figures