Cosmological constraints from the Hubble diagram of quasars at high redshifts

The concordance model (Λ cold dark matter (ΛCDM) model, where Λ is the cosmological constant) reproduces the main current cosmological observations1–4 assuming the validity of general relativity at all scales and epochs and the presence of CDM and of Λ, equivalent to dark energy with a constant density in space and time. However, the ΛCDM model is poorly tested in the redshift interval between the farthest observed type Ia supernovae5 and the cosmic microwave background. We present measurements of the expansion rate of the Universe based on a Hubble diagram of quasars. Quasars are the most luminous persistent sources in the Universe, observed up to redshifts of z ≈ 7.5 (refs. 6,7). We estimate their distances following a method developed by our group8–10, based on the X-ray and ultraviolet emission of the quasars. The distance modulus/redshift relation of quasars at z < 1.4 is in agreement with that of supernovae and with the concordance model. However, a deviation from the ΛCDM model emerges at higher redshift, with a statistical significance of ~4σ. If an evolution of the dark energy equation of state is allowed, the data suggest dark energy density increasing with time.