>I have a question: is it possible that someday a cosmology could be developed
>which involves an analogous situation? In other words, that no matter what
>the initial conditions (or for perhaps a broad range of possible conditions) a
>universe capable of supporting life would be the result? I suppose this
>would depend on whether the universe is a "driven, dissipative system". It
>isn't, is it?
Actually, in a sense, this is sort of the case already with the (currently
favored) models of inflationary cosmology. In such models there is a very
wide range of initial Big Bang initial conditions possible, with a wide
range of initial spatial curvatures--relatively empty open (hyperbolic)
space-times whose energy density is far lower than the critical value
necessary to close the universe, to very tightly curved closed universes whose
energy density is many times the value to close the universe. No matter what
the initial model is when the temperature of the universe falls to about
10^27 K (at a time of about 10^-35 s) after the BB the GUT gauge the universe
begins to undergo a phase transition (associated with the spontaneous
breakdown of the single GUT gauge group symmetry causing the GUT interaction
to split into the separate Strong interaction and the Electro-Weak
interaction (the gravitational interaction from the TOE had already split off
at about 10^-43 s after the BB at a temperature of about 10^32 K). As this
phase transition proceeds (from 10^-35 s to about 10^-24 s after the BB) the
latent heat released (from the GUT Higgs field acquiring a nonzero value)
reheats the universe and causes it to expand furiously in "size" or curvature
radius, so that at 10^-24 s post BB the universe could easily be have a
curvature radius 10^50 times larger than before. With such a large curvature
radius the universe is now effectively spatially flat and the energy density
is forced to just the critical value to close the universe to a precision of
one part in about 10^50. After 10^-24 s the rest of the BB Hubble expansion
proceeds as in nearly all hot BB models. (The Weak interaction splits off
from the EM interaction at about 10^-12 s post BB; the quarks produced are
confined into baryons at about 10^-6 s; the universe becomes transparent to
neutrinos at about 1 s; the primorial He is synthesized by 3 minutes; the
universe becomes transparent to photons by 10^6 yr, galaxies and stars next
form, and now it has been some 10^10 yr since the BB.)
Now today we don't know if the universe is spatially, 1 closed (i.e.
"spherically curved" and finite), 2 open (i.e. "hyperbolically curved" and
infinite), or 3 flat (i.e. uncurved and infinite borderline case between
the other 2 cases). The inflation theorists are betting that it is the flat
borderline case 3. Even if it is not flat the average energy density is
within 2 orders of magnitude of of the critical value necessary to be flat.
Without the inflationary era (10^-35 to 10-24 s post BB) if the universe
started out somewhat on the hyperbolic open side it would have expanded so
rapidly from the beginning to an asymptotically empty (heat dead) universe in
a very short time much shorter than the current age of the universe. There
would not have been enough time for gravity to cause stars and galaxies to
form before the finial ultra-diluted state was reached. If the universe
started out somewhat on the closed spherical side it would have quickly
expanded to its maximum size and recontracted to a Big Crunch well before
there was time again to form stars and galaxies. In order for the universe
to have been around in an interesting state for about billions of years it
is necessary for its initial energy density to be fine-tuned initially to
within about 1 part in 10^50 of the critical flat value. OTOH *with*
inflation it doesn't matter that the initial value was. The universe
automatically self-inflates until it is properly fine-tuned irregardless
of its initial energy density (at least irregardless over range of many
orders of magnitude). After it is sufficiently fine-tuned the Hubble
expansion continues in the normal way.
The inflationary theories also solve other fine-tuning problems
associated with the unnatural uniform smoothness of the universe regarding
it's initial density and it's temperature. The initial fluctuations in
these quantities need to be unnaturally fine-tuned unless there is the
inflationary era which makes it automatic.
>>Regarding Stan's comment about initial conditions, I think the hope of the
>>people in the field is that the ultimate theory will be so naturally
>>constrained by the requirements of maximal beauty, simplicity, and self-
>>consistency that only one boundary condition will be possible or compatible
>>with it. This is something like the motivation for Hawking's no-boundary
>>proposal for theories written in imaginary time. The idea is to have the
>>boundary condition as a natural part of the theory.
>===============================================================
>
>Can you elaborate on this last point? I've heard this before but don't
>understand how the boundary condition could emerge as a "natural part of
>the theory". Mathematically they are logically independent, aren't they?
This gets into very complicated and advanced mathematical waters well beyond
the purview of this list (and my competence). Suffice it to say that such
things usually come about from restrictions placed on the solutions of the
theory by topological constraints that appear from making analytic
continuations to different coordinate systems which make latent symmetries in
the theory explicit. The required topologies in the new highly symmetric
formulation strongly limit the kind of solutions possible. When analytically
continuing back to the original formulation in the old topology, new
restrictions may be placed on the boundary conditions of the theory. If the
restrictions are strong enough, the boundary conditions effectively become
determined. (I think that's how it works.)
David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us