Paul Steinhardt, one of the original cosmic-inflation theorists and the
man who coined the term "quintessence" has a new theory of cosmology
which is described at  The abstract

     The Cyclic Model is a radical, new cosmological scenario which
     proposes that the Universe undergoes an endless sequence of epochs
     which begin with a `big bang' and end in a `big crunch.' When the
     Universe bounces from contraction to re-expansion, the temperature
     and density remain finite. The model does not include a period of
     rapid inflation, yet it reproduces all of the successful predictions
     of standard big bang and inflationary cosmology. We point out
     numerous novel elements that have not been used previously which
     may open the door to further alternative cosmologies. Although
     the model is motivated by M-theory, branes and extra-dimensions,
     here we show that the scenario can be described almost entirely in
     terms of conventional 4d field theory and 4d cosmology.

The theory does not actually have a "big crunch" in the traditional sense;
rather, after a long period of expansion so that there is less than one
particle in each visible segment of the universe, a hidden dimension
contracts and suddenly the universe is full of light and energy, and it
starts expanding again.  There is no inflation as in the regular model,
instead the long period of expansion from the previous cycle is what is
responsible for the remarkable uniformity that is observed.

The interesting aspect from this list's perspective is how to regard
infinite-time cosmologies.  Does it make sense to imagine a universe
which has had an infinite past?  How could we simulate that on a computer,
if there were no starting point?

I think Steinhardt's model also allows for a spatially infinite, flat
universe as well.  So we have infinities in all directions, temporal as
well as spatial.

We could avoid the problem by postulating that every cycle in Steinhardt's
model is identical, giving the effect of a single universe, but I don't
think there is any reason in the theory to suppose that would happen.
Rather, each crunch is slightly different, and these small perturbations
carry over into unique initial conditions for the next big bang.

How could we go about modelling a universe like this?  Can we rule out
Steinhardt's cosmology on fundamental principles?  Are infinite-time
universes of zero measure compared to ones with a fixed beginning?
It would be interesting if the everything-exists model could be used to
constrain cosmological theorizing in this way.

Hal Finney

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