Quasars as high-redshift standard candles

The non-linear relation between the X-ray and ultraviolet (UV) luminosity in quasars has been used to derive quasar distances and to build a Hubble diagram at redshifts up to $z\sim$ 7. This cosmological application is based on the assumption of independence of the relation on redshift and luminosity. We want to test the reliability of this hypothesis by studying the spectroscopic properties of high-redshift quasars in the X-ray and UV bands. We performed a one-by-one analysis of a sample of 130 quasars at $z>$ 2.5 with high-quality X-ray and UV spectroscopic observations. We found that not only the X-ray to UV correlation still holds at these redshifts, but its intrinsic dispersion is as low as 0.12 dex (previous works reached 0.20$-$0.22 dex). For a sample of quasars at $z\sim$ 3 with particularly high-quality observations the dispersion further drops to 0.09 dex, a value entirely accountable for by intrinsic variability and source geometry effects. The composite spectra of these quasars, in both the X-rays and the UV, do not show any difference with respect to the average spectra of quasars at lower redshifts. The absence of any spectral difference between high- and low-$z$ quasars and the tightness of the X-ray to UV relation suggests that no evolutionary effects are present in the relation. Therefore, it can be safely employed to derive quasar distances. Under this assumption, we obtain a measurement of the luminosity distance at $z\sim$ 3 with 15 % uncertainty, and in a 4$\sigma$ tension with the concordance model.