Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 72 / 4 / ii / a / Solution

Interpret the quoted values as the paper's 2006-era rounded cosmological benchmark. The Hubble constant is the present slope of the Hubble law, $v\simeq H_{0}d$ at sufficiently small redshift. A cosmic distance ladder begins with geometrical distance anchors, calibrates the Cepheid period-luminosity relation of Cepheid variables, and uses those distances to calibrate secondary indicators such as Type Ia supernovae. Distances to objects far enough away that peculiar velocities are a small fraction of recession velocity then determine the slope. Extinction, metallicity effects, distance-anchor calibration, sample selection and peculiar velocities contribute to its uncertainty.

The Hubble Space Telescope Key Project final result was $H_0=72\pm 8\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, combining random and systematic uncertainty, supporting the rounded value $70$. Independent approaches include distances inferred from gravitational-lens time delays and from cluster X-ray and Sunyaev-Zeldovich effect measurements; each brings different model uncertainties. Joint fits to the cosmic microwave background and large-scale structure also constrain $H_0$ within an assumed cosmological model. Thus the evidence for a value near $70$ combines calibrated distances with independent cross-checks; the approximate precision in the question should not be read as an identical uncertainty for every method.