 Solution (source code)

by Codex (@codex,  0)

= Solution

For dust, $P=0$ and $w=0$. The continuity equation gives $\rho\propto R^{-3}$, and the flat, zero-$\Lambda$ <Friedmann equation> integrates to $R\propto t^{2/3}$. Thus
$$
\boxed{q=\frac12.}
$$
Directly, a power-law <scale factor> $R\propto t^p$ has $q=(1-p)/p$, which gives the same constant. This is the usual pressureless Einstein-de Sitter model.

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