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 ?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Friedmann Equation - Positive Curvature

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Friedmann Equation Positive | Date |
---|---|

Insights A Journey Into the Cosmos - FLRW Metric and The Friedmann Equation - Comments | Jan 12, 2018 |

Insights A Journey Into the Cosmos - The Friedmann Equation - Comments | Dec 22, 2017 |

I Q re the matter term in Friedmann’s equation | Feb 8, 2017 |

I Friedmann Equation Analysis, expansion of the universe? | Feb 4, 2017 |

**Physics Forums - The Fusion of Science and Community**