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Age & Size of Closed Cosmos are related ?

Widdekind
in Astronomy and Cosmology

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Please ponder a hypothetical closed Cosmos ([math]\rho > \rho_{crit}[/math]), composed completely of matter ([math]\Omega_M > 1[/math]). In (1+1)D, its spacetime diagram (x,t) would be spheroidal, 'circuloidally' [eliptically ?] closed in time (lines of longitude), and closed in space (lines of latitude).

 

Now, denser universes don't expand out as big, or for as long, as more rarified (but still cosmically closed) universes. Thus, the Radius of Curvature for Time, and the Radius of Curvature for Space, for a cosmically closed, matter only, universe, seem like they would be closely correlated.

 

Is this so, and is there any (simple) relation between the two ?

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