Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 310 / 1 / d

Measurements at many source redshifts directly sample the function $H_0[1+z-E(z)]$. In principle, sufficiently many precise and well-spaced measurements can fit $H_0,{\Omega }_{m,0},{\Omega }_{\mathrm{DE},0},w_0,w_a$ simultaneously; a single redshift supplies only one combination and cannot. In a spatially flat two-component model, ${\Omega }_{m,0}+{\Omega }_{\mathrm{DE},0}=1$, reducing the number of independent parameters by one. In practice the signal accumulated over ten years is extremely small and parameter degeneracies require broad redshift coverage and complementary data.