Supermassive black holes accreting matter at very high, perhaps even super-Eddington rates appear in the sky as a special class of luminous active galactic nuclei. These sources -- hereafter extreme quasars for brevity -- can be identified in relatively large numbers from major optical surveys over a broad range of redshifts thanks to selection criteria defined on the basis the so-called Eigenvector 1/quasar main sequence parameter space. The systematic trends of the main sequence are believed to reflect a change in accretion modes: at high accretion rates, an optically thick, geometrically thick, advection dominated accretion disk is expected to develop. Even if the physical processes occurring in advection-dominated accretion flows are still not fully understood, a robust inference from the models -- supported by a wealth of observational data -- is that extreme quasars should radiate at an extreme, well defined Eddington ratio with small scatter i.e., at a maximum radiative efficiency for a given black hole mass. This result makes it possible to derive redshift-independent "virial luminosity" estimates from measurements of emission line widths. The method relies on the estimate of the virial mass via a photoionization approach and is conceptually equivalent to the luminosity estimates based from line width in early and late type galaxies, and a sizeable sample of extreme quasars has the potential to yield an independent measure of the main cosmological parameters.
A major issue related to the cosmological application of extreme quasars is the identification of proper emission lines whose broadening is due to a virial velocity field over a wide range of redshift and luminosity. In addition, there are several caveats and missing pieces of informations before a rigorous standardization may become possible. Most relevant issues are the anisotropy of continuum emission and the geometry of the line emitting regions. Related concerns are the powerful high ionization winds, and the chemical composition of the line emitting gas. These issues are compounded with circumnuclear and host galaxy star formation that may also reach extreme levels, and with the presence of circumnuclear dust. While extinction due to dust does not seem to affect the rest frame UV and optical spectra of most sources, a fraction of them may still be partly embedded in a cocoon of gas and dust, and reddened to various extents. Nonetheless, large samples of extreme quasars can be built overcoming at least some statistical effects. We discuss several aspects related to a better understanding of their structure and of the complex interplay between accretion flow and line emitting region, as well as their formation and evolution from primordial epochs to the present-day Universe. We report on preliminary attempts to exploit extreme quasars as cosmological distance indicators, and we briefly discuss the perspective of the method and its extension over a broad range of redshift. Extreme quasars have the potential to provide a new class of distance indicators covering cosmic epochs from almost present day up to less than 1 Gyr from the Big Bang, much beyond the limits of other optical cosmological indicators such as supernovae.
