Going from the Newtonian to relativistic version of Friedmann's equation we use the substitution(adsbygoogle = window.adsbygoogle || []).push({});

[itex]kc^{2} = -\frac{2U}{x^{2}}[/itex]

The derivation considers the equation of motion of a particle with classic Newtonian dynamics. I can sought of see that if space is flat the radius of curvature will be infinite, so spatial curvature will vanish, but why exactly is |k| = 1 when space is not flat ?

Also I'm guessing that k is actually a ratio of something over that things absolute value, e.g.

[itex]k = \frac{thing}{\|thing\|}[/itex], because why else would it be +/- 1 or 0?

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# Why is the non-zero value of spatial curvature +/- 1?

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