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Holographic Gas and Dark Energy

Holographic Gas and Dark Energy. Miao Li Institute of Theoretical Physics 2009.03.19. Holographic dark energy The basic postulate of HDE is where L is some infrared cut-off. This formula is motivatde by the energy bound thus, this model of dark energy is called

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Holographic Gas and Dark Energy

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  1. Holographic Gas and Dark Energy Miao Li Institute of Theoretical Physics 2009.03.19

  2. Holographic dark energy • The basic postulate of HDE is • where L is some infrared cut-off.

  3. This formula is motivatde by the energy bound thus, this model of dark energy is called holographic dark energy model.

  4. The model was proposed more than 4 years ago, and has been studied extensively both theoretically and numerically. But, there has been no concretely proposal for the nature of this energy

  5. We made one such concrete proposal: The energy may be that of a unusual gas. (Miao Li, Xiao-Dong Li, Chunshan Lin and Yi Wang, Holographic Gas as Dark Energy, arXiv:0811.3332, Commun.Theor.Phys. 51:181-186,2009)

  6. 2008.12.29 Since the gas emulates a system with Gibbons-Hawking entropy, we call it a holographic gas.

  7. 2. The gas We start with the single particle partition function: where w is the degeneracy of particle with energy k.

  8. Let then the single particle partition is

  9. For a Maxwell-Boltzmann gas, the total partition is

  10. For other kinds of gas (Bose-Einstien and Fermi-Dirac): where

  11. When the chemical potential vanishes, we have simple relations

  12. Since the free energy thus the entropy scales as and if we use the Hawking temperature we wish the entropy to scale linearly in the area, then

  13. 2008.12.29 For all three kinds of gas, we have

  14. 2008.12.29 We deduce Or more generally for a modified dispersion relation

  15. 2008.12.29 Finally, for a gas in a ball of radius R, take the Hawking entropy and Gibbons- Hawking temperture we obtain

  16. 2008.12.29 Compare with the hoolographic dark energy model, we deduce To have a finite partition function, a>-3, thus c<1!

  17. 2008.12.29 What does c<1 mean? If we take R to be the radius of the future event horizon, we have a phantom dark energy model (see below). For a more general dispersion relation:

  18. 3. Stability of the gas The gas is stable. Three features guarantee this. (a) Positive specific heat

  19. 2008.12.29 (b) Positive mechanical pressure (c) Smallness of fluctuations

  20. 2008.12.29 4. Cosmology The evolution of holographic gas is dictated by the first law

  21. If R is a co-moving scale, we usually assume dS=0, then the effective pressure is equal to the mechanical one. But we SHOULD take R to be the radius of some kind of horizon, in general dS>0 thus the effective pressue can be negative!

  22. 2008.12.29 For instance, if then

  23. and

  24. 5. Infinite stastics Another kind of gas consists of all distinguishable particles

  25. Thus and c can be arbitrarily close to 1.

  26. Conclusion: A holographic gas is a viable model for dark energy, and gives rise to the holographic dark energy formula automatically. The gas is very unusual in that there is a huge degeneracy for low energy particles. This property is currently under close study.

  27. 2008.12.29

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