Cosmic Chronometers (Differential Ages)

The cosmic chronometer method measures the Hubble parameter H(z) directly from the ages of massive, passively evolving galaxies at different redshifts. The idea is elegant: if two galaxies formed at nearly the same time but are observed at slightly different redshifts, the difference in their ages divided by the difference in their redshift gives dz/dt — and hence H(z) — with no assumption about the expansion model. Using stellar population synthesis to extract ages from spectra, astronomers have compiled H(z) measurements from z ~ 0 to z ~ 2. The resulting curve is broadly consistent with ΛCDM, but the absolute normalization persistently prefers H₀ values in the range 72–74 km/s/Mpc, again higher than Planck's early-universe determination.

The tension has two faces. First, the high H₀ values from cosmic chronometers align with SH0ES and H0LiCOW, adding a fourth independent method pointing away from the Planck result. Second, the H(z) measurements at intermediate redshifts (z ~ 0.5–1.0) show mild but systematic offsets from standard ΛCDM predictions even when H₀ is left free — hinting that the expansion history itself may not follow the expected ΛCDM trajectory. Systematic uncertainties in the stellar ages from spectral models are acknowledged, but multiple independent stellar population codes yield consistent results. ΛCDM cannot explain why every rung of the late-universe distance ladder independently points to a faster expansion rate than the early-universe CMB demands.