= Age ordering of dust universes at fixed Hubble parameter
{title2=$t_{\rm closed}<2/(3H_0)<t_{\rm open}<1/H_0$}
For an expanding <pressureless matter> universe with zero <cosmological constant>, fixed current <Hubble parameter> $H_0$ and current matter <cosmological density parameter> $\Omega>0$, the <age of a dust universe without a cosmological constant> is $H_0t_0=\int_0^1\sqrt{x}/\sqrt{\Omega+(1-\Omega)x}\,dx$. For every $0<x<1$ the integrand decreases strictly as $\Omega$ increases. Thus open models with $0<\Omega<1$ are older than the flat model, and closed expanding models with $\Omega>1$ are younger. The flat value is $2/3$ and the empty <Milne universe> limit is $1$. Specifying what is held fixed matters: at fixed present <scale factor> and <energy density>, the integral $t_0=\int_0^{a_0}da/\sqrt{C/a-k}$ instead increases with $k$, provided all three models reach $a_0$ on their expanding branches.
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