WMAP and Big Crunch: Is the Universe's Fate Sealed?

[vincentm]

Hello all,

With the results of the WMAP survery of the CMB back in march of this year, has this ruled out the possibility of the universe undergoing a "big crunch"?

I've read somewhere that the average density of matter in the universe has been measured to be

p=1

Is this right?

 

[hellfire]

In an universe without dark energy, an average energy density above the critical density would lead to a big-crunch, and an average energy density below or equal to the critial density would lead to an eternal expansion. However, with dark energy things are different. An universe with average energy density above the critical density may expand forever. This is because dark energy exterts a pressure that accelerates the expansion of space.

The average energy density measured by WMAP is equal to the critical density $\Omega = \rho / \rho_{crit} = 1$. Even if it would be slightly above the critical energy density, our universe would expand forever. I remember that a time ago I tried some calculations to find out what is the lowest value for the relation between the energy density of matter and the energy density of dark energy (assuming it to be a cosmological constant) for which a closed expanding universe will start contracting: if there is enough matter the expanding universe will start contracting regardless of the effect of dark energy and before it starts becoming dominant. I could not find this calculations now, but if you are interested we could try to figure it out.