Quasar Hubble-Diagram Deviation at z > 1.5

Type Ia supernovae run out at redshift z of about 1.5, leaving the expansion history of the universe untested by standard candles across most of cosmic time. Risaliti and Lusso extended the Hubble diagram to z of 5 using quasars, standardized through the nonlinear relation between their ultraviolet and X-ray luminosities (L_X proportional to L_UV to the power gamma with gamma of about 0.6), a relation whose intrinsic dispersion drops to 0.20 to 0.25 dex once dust-reddened, gas-absorbed, and Eddington-biased objects are removed. The result is a clean test of ΛCDM where it has never been tested, and the test fails: the quasar Hubble diagram agrees with supernovae and with the model at z below 1.4, then deviates progressively at higher redshift, with the joint supernova plus quasar analysis excluding the flat ΛCDM expansion history at about 4 sigma (Risaliti and Lusso 2019, Nature Astronomy; Lusso et al. 2019, arXiv:1907.07692, which reaches over 4 sigma adding gamma-ray bursts).

ΛCDM has no freedom to bend its high-redshift expansion: once the parameters are fixed by the CMB, BAO, and low-z supernovae, the luminosity distance at z of 2 to 5 is fully determined by the constant-Lambda Friedmann equation. The observed deviation, read at face value, says the real universe expanded differently in the matter-dominated era than constant Lambda allows, in a direction consistent with the evolving dark energy hints DESI later found at low redshift. The model can only respond by attacking the probe: Khadka and Ratra (2020-2022) and others argue the L_X-L_UV relation parameters evolve with redshift or suffer selection effects, rendering quasars unusable for cosmology.

The probe has held up better than the criticism expected. Lusso et al. (2025) and the eROSITA quasar analysis show the X-ray to UV relation remains stable across samples, instruments, and redshift once selection is controlled, and that dismissing the tension requires the relation to change character abruptly at z of about 1.5, exactly where supernovae run out and the deviation begins, which would itself demand an unexplained coincidence in accretion physics. The standing is therefore contested but live: either quasars are revealing a genuine high-redshift departure from ΛCDM, or an accretion-physics conspiracy mimics one precisely where no independent check exists. Euclid spectroscopy, JWST-calibrated high-z supernovae, and larger X-ray samples will decide.

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