Cosmology with z>3 quasars

We have recently shown that the nonlinear correlation between Xray and UVemission in quasars can be used to estimate quasar distances with a precision ofvirgul0.2virguldex. This allows to build a Hubble Diagram for quasars up to zvirgul6, opening anew window of observational cosmology at high redshift. Here we propose toobserve a sample of 30 quasars at zvirgul3, in order to estimate the ratio of theexpansion of the Universe at z3 and zvirgul0.5 with a 10% precision, enough for atight test of the standard cosmological model, and to improve the currentconstraints on the possible evolution of the equation of state of dark energy. truncated!, Please see actual data for full text [truncated!, Please see actual data for full text]