The measured <Hubble time> would give the Einstein-de Sitter age
$$
t_0=\frac23(14\ {\rm Gyr})\simeq9.3\ {\rm Gyr},
$$
which is less than the measured $12\ {\rm Gyr}$ age of stars that must themselves be younger than the universe. The measurements are therefore incompatible with an <Einstein-de Sitter universe>. For the stated spatially flat <Lambda-CDM model>, direct evaluation of the preceding integral gives
$$
H_0t_0=\frac{2}{3\sqrt{0.7}}\operatorname{arsinh}\sqrt{\frac{0.7}{0.3}}\simeq0.964,
$$
and hence $t_0\simeq13.5\ {\rm Gyr}$. The period of <accelerating expansion> caused by the <cosmological constant> therefore allows an age consistent with the stellar lower bound.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 310 / 1 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-310/1/d/solution