Re: Cosmology

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding Bob Zannelli's comments:

> ... Let me postulate a Universe empty of any
> mass that is spatially flat. I believe this is a formulation known as the De
> Sitter Universe. General Relativity implies the following equation.
>
>         ((da/dt)^2)*(1/((a^2)*(c^2))+k/(a^2)-A=8*pi*G*p/(3*(c^4))
>
>  Where a is the scale factor, k is curvature, A is the cosmological constant
> and p is mass-energy density. In a Universe that is spatially flat (K=0) and
> has zero energy density (p=0) by solving the above equation we get the
> following result:
>
>           a=ki*exp((A^.5)*c*t Where Ki is an arbitrary constant.
>
> which suggest under the condition of a spatially flat Universe with zero mass
> energy density we end up with an expodential expansion of the scale factor.
> This looks a lot like inflation though this approach is really an
> oversimplified example.

This is completely correct.  I alluded to it in my last post (in a part
that you didn't quote) where I discussed what happens to an expanding
universe that is spatially flat (& homogeneous & isotropic) in the
asymptotic future with a positive CC.  In that limit the matter becomes
so diluted that for all practical purposes the expansion is determined
entirely by the CC, and the limiting behavior is that of an exponential
expansion of the scale factor.  Such a universe inevitably *becomes* a
DeSitter universe in its future limit.  (And, apparently, it seems that
our universe *is* such an example).

David Bowman
David_Bowman@georgetowncollege.edu