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where <math>\Omega</math> is the mass-energy density fraction of the universe. Specifically, <math>\Omega = \rho/\rho_c</math>, where <math>\rho_c</math> is the ''critical'' mass density, above which the universe would be closed and destined to collapse.
 
where <math>\Omega</math> is the mass-energy density fraction of the universe. Specifically, <math>\Omega = \rho/\rho_c</math>, where <math>\rho_c</math> is the ''critical'' mass density, above which the universe would be closed and destined to collapse.
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The integral of the above equation, expressed in dimensionless numbers, is:
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The integral of the above equation, expressed in [[dimensionless]] numbers, is:
    
<math>\frac{r}{c\tau} = \frac{\sinh(\beta \sqrt{1-\Omega})}{\sqrt{1-\Omega}}</math>
 
<math>\frac{r}{c\tau} = \frac{\sinh(\beta \sqrt{1-\Omega})}{\sqrt{1-\Omega}}</math>
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