= Solution
For <pressureless matter>, the <Friedmann acceleration equation> with vanishing <cosmological constant> is
$$
\frac{\ddot a}{a}=-\frac{4\pi G}{3}\rho_m.
$$
Evaluating at the present <cosmic time> and using the definition of the <deceleration parameter> gives
$$
q_0=\frac{4\pi G\rho_{m,0}}{3H_0^2}
=\frac12\frac{\rho_{m,0}}{3H_0^2/(8\pi G)}.
$$
The denominator is the <critical density>, so the <cosmological density parameter> satisfies \b[the dust relation]
$$
\boxed{\Omega_{m,0}=2q_0.}
$$
This uses <pressureless matter> and $\Lambda=0$; spatial flatness has not been assumed.
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