Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2017 / S2 / 3 / 2 / Solution

Set the spatial-curvature constant to zero in the stipulated matter-only Friedmann equation to get ${\rho }_c=3H^2/(8\pi G)$. Conservation of pressureless matter with $R(t_0)=1$ gives $\rho ={\rho }_0/R^3$, and thereforeChoosing the Big Bang as $t=0$ yields $R=(t/t_0{)}^{2/3}$ and $H=2/(3t)$. Consequently $\boxed{t_0=2/(3H_0)\simeq 9.3\mathrm{Gyr}}$ for the supplied $H_0$. This is the age of the flat pressureless model without a cosmological constant, not a determination in the current multi-component cosmological model.