Friedmann Equation without the cosmological constant can be written as;(adsbygoogle = window.adsbygoogle || []).push({});

$$H^2=\frac {8πρG} {3}-\frac {1} {a^2(t)}$$

for ##Ω>1## (which in this case we get a positive curvature universe), and for a matter dominant universe;

$$ρ=\frac {1} {a^3(t)}$$

so in the simplest form the Friedmann equation becomes;

$$H^2=\frac {1} {a^3(t)}-\frac {1} {a^2(t)}$$

For a(t) larger than 1. The equations becomes negative but I remember that

Proper distance is proportional to a(t), ##D=a(t)Δx## so when ##a(t)## is smaller then ##1## it means universe collapses. In this case how it expends in the first place ?

##a(t)## is a function of ##t## so in this sense even its get smaller its possible that to get expand and then collapse I think but how can I find it ?

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# I Friedmann Equation - Positive Curvature

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