>Stan Szygmunt wrote:
>
>>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?
>
David Bowman responded:
>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
>
My question is: David's response focused on the issue of curvature. But
what about other matters such as the values of physical constants, masses of
elementary particles, relative strengths of forces, etc. Are these dependent
on inflation? What governs their values? To what extent do they depend on
initial conditions?
Larry Funck
Chemistry Dept.
Wheaton College
Wheaton, IL 60187