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Yes, this is correct, which is why we can say it is definitively ruled out by current observations. We don't need to bother to modify anything to examine the Milne model: we merely compare our parameter estimates and see if the "total density = 0" case is ruled out. And it is to around 100 standard deviations with a combination of baryon acoustic oscillation and WMAP data (with this combination of data, $\Omega = 1$ to within about a percent at one standard deviation).