I How many apparent horizons could the Universe have?

[Suekdccia]

TL;DR Summary

Different universes in different apparent horizons?

I was reading a paper written by George Smoot [1], which assumes the holographic principle as true and conjectures that our universe would be encoded on the "surface" of an apparent horizon as the weighted average of all possible histories. In that way, there would be one world (or universe) that would be the average among all possible worlds.

However, could more than one apparent horizon exist? And if the answer is affirmative,then, wouldn't there be other universes "encoded" on those other apparent horizons if that was the case? And could some of these other universes be the result of the realization of one particular history (or of a particular set of histories) instead of the average of all possible histories?

[1]: https://arxiv.org/abs/1003.5952

 

[PeterDonis]

could more than one apparent horizon exist?

Yes and no.

In our universe, each observer has one cosmological horizon (which is what "apparent horizon" means in the context of this paper). But different observers at different spatial locations have different cosmological horizons.

Note that this means that the paper's use of the term "the apparent horizon of the universe" is not really correct. Our universe does not have one apparent horizon; it has an infinite number, one corresponding to each spatial location.

If what is actually mean is "the apparent horizon of our observable universe", then there is just one of those and the paper's analysis would apply to our observable universe. But our observable universe is not the same as the universe as a whole.

 

[Suekdccia]

Yes and no.

In our universe, each observer has one cosmological horizon (which is what "apparent horizon" means in the context of this paper). But different observers at different spatial locations have different cosmological horizons.

Note that this means that the paper's use of the term "the apparent horizon of the universe" is not really correct. Our universe does not have one apparent horizon; it has an infinite number, one corresponding to each spatial location.

If what is actually mean is "the apparent horizon of our observable universe", then there is just one of those and the paper's analysis would apply to our observable universe. But our observable universe is not the same as the universe as a whole.

Okay. And then, another Hubble sphere (aka another observable universe) would have another apparent horizon, right?

 

[PeterDonis]

another Hubble sphere (aka another observable universe) would have another apparent horizon, right?

Yes.

 

[Suekdccia]

Yes.

Another question related to this:

As the universe keeps expanding we'll see fewer structures (like galaxies) until we'll reach a point where we wouldn't see any structures that would not be gravitationally bounded to us. Since this would happen also to every other galaxy (or groups of sufficiently near galaxies) then, would in the future each galaxy (instead of huge Hubble spheres) have its own cosmological horizon?

 

[PeterDonis]

would in the future each galaxy (instead of huge Hubble spheres) have its own cosmological horizon?

You are thinking of this backwards. It isn't that Hubble spheres stop being "huge" and get small enough to only have one galaxy in each of them. What happens is that accelerated expansion, from the standpoint of any given galaxy (or more precisely gravitationally bound system), carries all other galaxies (other systems not gravitationally bound to yours) out beyond your cosmological horizon--and similarly, from their standpoint, you are carried out beyond their cosmological horizon. The proper distance to your cosmological horizon continues to increase (though it asymptotes to a finite distance, it does not increase without bound).

 

[KobiashiBooBoo]

Eventually a viewer from every galaxy (or bound system) would see nothing on the horizon? (Assuming enough time passes and each galaxy does not turn into a giant black hole). An observer would not see a 3K degree background radiation, it would eventually be close to, but never reach, zero Kelvin?

 

[PeterDonis]

Eventually a viewer from every galaxy (or bound system) would see nothing on the horizon?

Since you are including background radiation, no, this is not correct.

An observer would not see a 3K degree background radiation, it would eventually be close to, but never reach, zero Kelvin?

No. A cosmological horizon has a finite temperature. The background radiation you see will never drop below that temperature; it will just eventually be due to the cosmological horizon instead of the CMBR.

 

[Suekdccia]

No. A cosmological horizon has a finite temperature. The background radiation you see will never drop below that temperature; it will just eventually be due to the cosmological horizon instead of the CMBR.

That is interesting. Has this been observed or tested experimentally or is it only a theoretical prediction?

 

[PeterDonis]

Has this been observed or tested experimentally or is it only a theoretical prediction?

It's only a theoretical prediction at this point. The temperature of our cosmological horizon is far too low (about $10^{-30}$ K) for us to detect the corresponding radiation.

 

[Vanadium 50]

temperature of our cosmological horizon is far too low

And will be swallowed up by the ordinary CMBR. At all frequencies the CMBR will put out more eneegy.

Indeed, given the CMBR variations, I question whether it could be seen even in principle.

 

[PeterDonis]

And will be swallowed up by the ordinary CMBR.

Now, yes. But at some point in the future the CMBR temperature will drop below the horizon temperature.

 

[Vanadium 50]

OK, who wants to wait 10⁴⁰ years for the answer? Hands please!