Past exam of the mathematics course of the University of Cambridge 2006 iii Paper 72 4 ii a Solution Created 2026-10-03 Updated 2026-10-14
Interpret the quoted values as the paper's 2006-era rounded cosmological benchmark. The Hubble constant is the present slope of the Hubble law, 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 , combining random and systematic uncertainty, supporting the rounded value . 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 within an assumed cosmological model. Thus the evidence for a value near combines calibrated distances with independent cross-checks; the approximate precision in the question should not be read as an identical uncertainty for every method.