Cyclic Universe, Big Rip version

[Dmitry67]

I wonder if someone has ever considered the following scenario:

1. "Standard" Big Rip model (phantom energy-dominated)
2. Close to the Big Rip, Universe becomes crossed with Cosmological horizons
3. Based on semiclassical approach, these horizons emit Hawking radiation
4. As a (slightly retarded) reaction to rapid expansion, Universe becomes filled with radiation (=matter)
5. And it becomes matter-dominated (as reaction is retarded, when matter stops the expansion, there is more matter then was required to perfectly balance the Dark Energy)
6. The mattter keeps expanding (as an 'echo' of a previous aeon)
7. This sequence repeats over and over again. Big bang = previous Big Rip

Note that this approach does not have any problems with entropy.

 

[Chalnoth]

I wonder if someone has ever considered the following scenario:

1. "Standard" Big Rip model (phantom energy-dominated)
2. Close to the Big Rip, Universe becomes crossed with Cosmological horizons
3. Based on semiclassical approach, these horizons emit Hawking radiation
4. As a (slightly retarded) reaction to rapid expansion, Universe becomes filled with radiation (=matter)
5. And it becomes matter-dominated (as reaction is retarded, when matter stops the expansion, there is more matter then was required to perfectly balance the Dark Energy)
6. The mattter keeps expanding (as an 'echo' of a previous aeon)
7. This sequence repeats over and over again. Big bang = previous Big Rip

Note that this approach does not have any problems with entropy.

Step four can't occur in this way. Basically, the expansion dilutes the universe so well that it just stays empty.

The way that the "big rip" scenario would work is that within the big rip scenario, there is actually a singularity of infinite expansion rate in the finite future. The idea would be that this singularity is unphysical, and instead maps onto inflation, which decays and starts a new universe.

The problem is, I don't think anybody has been able to propose a model that actually does this.

 

[Dmitry67]

Why?
Step 4 - do you disagree that Universe becomes filled with matter?
or you claim that the rate of expansion is so fast that hawking radiation can't dominate over phantom energy?

Note: hawking radiation is EXTREMELY intensive, and the only reason why the flow from black holes is so tiny is the enourmous red shift. But from the cosmoloical horizons there is no red shift.

 

[Chalnoth]

Why?
Step 4 - do you disagree that Universe becomes filled with matter?
or you claim that the rate of expansion is so fast that hawking radiation can't dominate over phantom energy?

Yes. The radiation dilutes just as fast as it is produced, and so never dominates over the vacuum energy.

Note: hawking radiation is EXTREMELY intensive, and the only reason why the flow from black holes is so tiny is the enourmous red shift. But from the cosmoloical horizons there is no red shift.

There is, however, redshift due to the expansion.

 

[Dmitry67]

Fast expansion just means small hublle bubbles and very close horizons which means very intensive radiation.

In any case I guess it is time for formulas.

 

[Dmitry67]

Also note that horizons emit radiation proportional to Temperature^4, and T depends of a distance to horizon (so wavelength have the length approx equal the distance to the horizon). So no matter how fast curvature increases, the density of matter increases much (T^4) faster.

 

[Chalnoth]

Also note that horizons emit radiation proportional to Temperature^4, and T depends of a distance to horizon (so wavelength have the length approx equal the distance to the horizon). So no matter how fast curvature increases, the density of matter increases much (T^4) faster.

That makes its energy density as a fraction of the dark energy density invariant with respect to horizon scale.

 

[Dmitry67]

Why?
What is density of DE if we know that bubble radius is R?

 

[Chalnoth]

Why?
What is density of DE if we know that bubble radius is R?

The Hubble radius is $r_h = c/H$, and $H$ is given by:

$$H^2 = {8 \pi G \over 3}\rho$$

So the density is:

$$\rho = {3 \over 8\pi G}\sqrt{c \over r_h}$$

The temperature is proportional to the inverse of the radius (I don't know the constants offhand), so the Hawking radiation temperature would be proportional to the square of the dark energy density. So I guess I was mistaken that the energy density fraction in Hawking radiation is invariant with respect to the dark energy (I did some unit analysis in my head, apparently incorrectly). I think this is accurate:

$$\rho_{\mathrm{DE}} \propto \sqrt{T}$$

and

$$\rho_r \propto T^4$$

so:

$$\rho_{\mathrm{DE}} \propto \rho_r^{1/8}$$

So you're right, for large values of dark energy, the radiation density would overwhelm the dark energy density. However, there is a problem with this: the radiation from the horizon assumes dark energy density domination. Once the radiation density becomes comparable to the dark energy density, this assumption is broken. So it's still not clear to me that the Hawking radiation actually could overwhelm the density, because doing so would eliminate the Hawking radiation.

 

[Dmitry67]

Thank you for the confirmation. Now where is my Nobel prize? :)

I also agree with the last part, my guess is that the system will pass the point of balance and becomes matter dominated, keeping expanding rapidly. Exactly the Big Bang...

 

[Chalnoth]

Thank you for the confirmation. Now where is my Nobel prize? :)

I also agree with the last part, my guess is that the system will pass the point of balance and becomes matter dominated, keeping expanding rapidly. Exactly the Big Bang...

But to do that, you have to have some sort of interaction that stops the dark energy from continuing to grow in density. You still have the problem under this scenario of a singularity in the finite future of infinite expansion rate. You can grow the radiation density all you like, but without getting rid of the dark energy density, the total energy density will simply continue to grow without bound.

 

[Dmitry67]

Grrrrrrr...
I am only few years late:

http://en.wikipedia.org/wiki/Cyclic_model

The Baum–Frampton model

This more recent cyclic model of 2007 makes a different technical assumption concerning the equation of state of the dark energy which relates pressure and density through a parameter w.[5][8] It assumes w < −1 (a condition called phantom energy) throughout a cycle, including at present. In the Baum–Frampton model, a septillionth (or less) of a second before the would-be Big Rip, a turnaround occurs and only one causal patch is retained as our universe. The generic patch contains no quark, lepton or force carrier; only dark energy – and its entropy thereby vanishes