Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 310 / 1 / d

All galaxies in the population share the same formation time $t_f$, so the difference between their stellar ages equals the difference between their cosmic emission times. The redshift-time relation givesFor a close pair with $|\Delta z|\ll 1$,A cosmic chronometer measurement therefore reconstructs $H(z)$ directly from differential galaxy ages. Inserting those values into the matter-plus-dark-energy Friedmann expression constrains $w(z)$.

Supernova distances integrate $1/H(z)$, while $H(z)$ already contains an integral of $w(z)$. Cosmic chronometers avoid the distance integral, so rapid oscillations in $w(z)$ suffer one fewer smoothing operation and can leave a more visible signal.