Stathis -
> I would have guessed 
> that as the universe expands, chemical and nuclear reactions are less likely 
> to occur, in the same way as chemical reaction rates are proportional to the 
> concentration the reagents. On the other hand, it is not clear to me how 
> more exotic processes such as spontaneous appearance of particles out of the 
> vacuum are affected by the expansion, which after all results in "more 
> vacuum" - doesn't it?

We had some discussion a while back about a paper which proposed some
similar ideas,, Disturbing
implications of a cosmological constant.  If you want to look in the
archives, the thread was called "Doomsday-like argument in cosmology"
and was in August 2002.

According to this paper, if there is a cosmological constant then
the expansion of the universe will accelerate and eventually reach
what is called a de Sitter state, where it is expanding exponentially.
However the authors suggest that we could simply imagine our yardsticks
also expanding exponentially, and the universe would then be in a
steady state.  In a steady state universe, fluctuations such as you
describe will occur and all possible universes will eventually exist,
in fact they will come into existence an infinite number of times.

Now, I never really understood the physics involved here.  I tried
to learn about de Sitter universes and the data I got was somewhat
contradictory.  Some writers suggested that the mass density was zero in
such a universe.  It certainly seems odd to suggest that the yardsticks
can expand without realizing that this would cause particles to appear to
contract, presumably with physical implications similar to the questions
you raise.

However the authors were physicists and supposedly know their stuff.
So maybe it is true that even in our current cosmological models, random
fluctuations will be able to bring future universes into existence.

The point of this paper was that in that case, since such universes occur
an infinite number of times, it is infinitely unlikely that we should
find ourselves in the first one, the "original" universe which is evolving
from the Big Bang and just transitioning into the de Sitter expansion.
Hence, on anthropic principles, this is a contradiction.

One might propose to resolve it by suggesting that in fact we don't live
in the primordial universe, but are in one of the fluctuations.  However
this doesn't work, because fluctuation universes are overwhelmingly
likely to look very different from our universe.  The chance that an
observer in a fluctuation universe would see a past that was consistent
with a Big Bang is essentially zero.  So again, the anthropic principle
seems to indicate that our observations are inconsistent.  We can't
both observe a universe with an infinite number of (eventual) observers,
and see ourselves in such a unique position.

I still wonder about the physical assumptions that treat the de Sitter
state as a steady state.  That little coordinate transform seemed pretty
fishy to me.  I don't know if this paper ever got peer reviewed but I'd
take it a lot more seriously if or when that happens.

Hal Finney

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