Heaven’s Parameters

Oh… I forgot to get around to letting you know the result of designing the universe required in a previous post. The result is that it is a radiation (“light”) filled universe with positive cosmological constant [tex]\Lambda[/tex] (and so space wants to expand due to negative pressure – much like ours seems to be doing). The radiation density wants the thing to collapse. There’s a balance between the two, and it turns out that it is when the two densities (radiation, and vacuum energy) are equal. This is only possible when there is positive curvature for the universe (so, not like ours), as you can see from the Friedman equation if you were that way inclined. So the universe is a 3-sphere, and if you work it out, the radius of this 3-sphere turns out to be [tex]a=\left(\frac{3}{2\Lambda}\right)^{1/2}[/tex]. The temperature of the radiation is then computed using the usual Stefan-Boltzmann relation.

The equality of densities turns out to result from the fact that the effective potential of the equation is at a maximum, and so this universe turns out to be unstable… It is a radiation-filled version of Einstein’s matter-filled static universe, which is also unstable. It is larger than Einstein’s by a factor of [tex]\sqrt{3/2}[/tex].

Einstein was said to have arrived at his static universe on the grounds of what he thought was observationally clear – the universe was unchanging (on large scales). Hubble had not yet observed the expansion of the universe. (Note that it was most likely not due to some internal prejudice he had about the meaning of a changing universe, as is often said… it was simply a reasonable thing to assume, and try finding a solution for, at the time, in retrospect.)

Lastly, I hope it was clear I was joking about this universe being Heaven! (I say that in light of a letter I got from a viewer of the TV show The Universe that I appear on, reminding me that I should mention to people from time to time that science is perhaps not the place to look for answers as to where lost loved ones have gone… Well, put differently, it is not really the motivation of the scientists I know. That’s an entirely different department.)

It’s obviously not Heaven because I’ve not included the equation of state for angel wings, harps, and so forth, have I? Anyone know what the function [tex]p_{\rm a.w.}(\rho_{\rm a.w.})[/tex] might be? 🙂

-cvj