Any comment as to why that paper is relevant, Sean?

in your paper hep-th/0410270 with Chen, you discuss a bit about unitary time evolution. This reminded me of this problem (I don’t work in this field so perhaps it is trivial):

If you start out with a region of some finite volume then presumably here are only a finite number of fundamental states available for that volume. If this region undergoes expansion and becomes larger, then shouldn’t there be less degrees of freedom available per unit volume if you demand unitary time evolution?

But if one thinks of the standard model as an effective low energy theory obtained by integrating out the fundamental degrees of freedom, then this means that the coupling constants would have to change according to a renormalization group transformation.

Or is this just an artefact of treating the expansion clasically? Is the density of states in the original space time for which the scalar field configurations are compatible with the expansion just the same as in the final space time?

Anyway I wanted to divert attention for 1 second and show the status of discrete functions in our cosmo? Does it have sound reasoning?

Are topological functions natural? I was creatively inspired.

Now back to regular programming. Thanks

Except for accelerated expansion (ala inflation or dark energy), there’s nothing that drives spatial hypersurfaces to be flat.

I’m pretty sure that a balance between gravity and the expansion will accomplish that in this case, which was my point, where the simplist version of infationary theory was tacked-on to big bang theory in order to explain a lack of causal connection in the universe given the uniformity of cosmic background radiation and the size of the universe… which I just did, as well, but without the need for the bandaid theory.

Occam would tell you that causality is not violated if the universe has volume when a big bang occurs, so you should not assume idealized theoretical projections beyond that, (which require that we accept even more unproven theoretical speculation), without very hard proof, which I do not believe that you have.

I don’t believe that you can prove that Einstein’s static model was unstable either, since matter generation from vacuum energy in that model will cause a counterbalancing increase in negative pressure and positive gravitational curvature. The fact that Einstein did not know about real particle potential in the quantum vacuum does not change the fact that he’s still right until somebody proves him wrong, since this process causes expansion in this model.

It is easily shown that a counterbalanced increase between negative pressure and positive gravitaional curvature causes tension between the vacuum and ordinary matter to increase while the universes is held flat and stable by this effect which will lead to the previously described scenario for pre-existing volume when the forces that bind the universe give-way to the straw that breaks its back, so there will again be no violation of causilty, AGAIN… and occam is still a happy camper.

I’ve made this point before, but it didn’t capture your interest, so I can only assume that this means that you don’t see how this might affect other assumptions that have been made which are also taken for granted to disprove or supercede this model.

I disagree with that too, because the interpretations of what the evidence means change in this model, as well.

Elliot– people have thought about linking inflation and dark energy, e.g. Peebles and Vilenkin. But the energy scales are so fantastically different that it doesn’t seem like a match made in heaven.

Island– if you want to think about the spatial geometry of the universe as an harmonic oscillator, it’s an upside-down oscillator; flatness is an unstable point. Except for accelerated expansion (ala inflation or dark energy), there’s nothing that drives spatial hypersurfaces to be flat.

Again forgive the layman’s naivete here but.

Since the “inflaton” field drives the inflationary expansion and Dark Energy seems to be driving the acceleration of expansion in our universe, is there any line of reasoning that might suggest these two are related or are we talking apples and oranges here?

Thanks,

Elliot

It’s because the rate of expansion of the false vacuum is so extremely fast. If you start out with a small piece of false vacuum that is inflating then there is always a small probability that a piece of it won’t have decayed to the normal state.

The survival probability of a piece of the false vacuum goes to zero exponentially, but the total volume of the false vacuum increases exponentially. The product of the two factors grows exponentially, so the total volume of inflating false vacuum keeps on growing forever.

See also here:

http://online.itp.ucsb.edu/online/kitp25/guth/oh/06.html

OK,thanks! So I guess the next question is: why should we believe in inflation that is eternal rather than inflation that happens *once* after a [finite] universe was born? I’ve seen claims that eternal inflation is “generic” but I can’t even imagine what that could mean…

I can never seem to wrap my head around this because it seems to me that our universe *is* the most natural configuration if you consider that flatness represent’s the damping of an imperfect quantum harmonic oscillator, where non-unitary dissipative evolution prevents an inherently imbalanced density matrix from evolving inhomogeneously, since the second law dictates a tendency toward uniform mass distribution.

Entropy as a measure of the uniformity of the distribution of energy tells us that complete entropy, (with all matter and energy distributed over maximally expanded spacetime), requires the formation of far-from-equilibrium dissipative structures in order for the total mass distribution in an imperfect world to become *progressively* more-uniform, so a near-flat universe is most natural… if there is inherent asymmetry.