Holographic Dark Energy and Anthropic Principle Qing-Guo Huang Interdisciplinary Center of Theoretical Studies CAS

I. Dark Energy Problem

Why the order of magnitude of the dark energy density is much smaller than quantum corrections in local effective field theory?

Why the dark energy density is the same order as today’s critical energy density of our universe? – Called the cosmic coincidence problem.

II. Holographic dark energy Cohen, Kaplan and Nelson, Phys. Rev. Lett. 82 (1999) Effective field theory describes all states of the system excluding those for which have already collapsed to a black hole.

Further they proposed that energy density is

Hsu, Phys.Lett. B. 594 (2004) Taking L as the Hubble scale, the resulting energy density is comparable to the present dark energy density. But the equation of state w=0 is disfavored by observational data.

M. Li, hep-th/ Li suggested that we should take L as the proper size of the future event Horizon.

M. Li, hep-th/ ; Q. G. Huang and Y. G. Gong, JCAP 0408 (2004) 006 ; Q. G. Huang and M. Li, JCAP 0408 (2004) 013. For d=1, the holographic dark energy sounds like cosmological constant when it dominates the evolution of universe. We found that the equation of state of the holographic dark energy is always w=-1/3 when any other type of energy dominates the evolution of universe.

The evolution of in a universe with matter and dark energy is

The equation of state The red line : The blue line :

III. Anthropic Principle No one asks the dark energy problem if the astronomers can not exist at all.

In the inflation scenario, our observed universe is a tiny patch in the early universe and the whole space- time may contain many disconnected regions which will grow up to many sub-universes. This offers a framework for applying the anthropic principle. With developments in string compactifications, there are so many vacua to favor the working of the anthropic principle.

Weinberg, Phys. Rev. Lett. 59 (1987) 2607; At recombination, the Anthropic bound on the cosmological constant is whereis the energy density fluctuation at recombination.

Martel, Shapiro and Weinberg, Astrophys. J. 492 (1998) 29. The probability distribution of the dark energy is whereis the mean number of astronomers who can measure the dark energy density in a subuniverse. Sinceis much smaller than the energy scales in the theory of elementary particle physics, we usually assume a priori probability distribution is a constant.

The number of astronomers should be proportional to the fraction of matter incorporated in galaxies. where s is the ratio of the volume of the over-density sphere to the volume of the under-density shell surrounding the sphere. Usually we set s=1.

We assume the fluctuation distribution is Gaussian distribution A useful result

The variance whereis the power spectrum as recombination, is a Gaussian window function, R is the minimal size of structures that are relevent in providing environment for emergence of intelligence. We don’t really know the sufficient condition for the formation of astronomers. We assume the order of the magnitude of R be around 1 Mpc.

Aguirre, Phys. Rev. D64 (2001) ; Tegmark and Rees, Astrophys. J. 499 (1998) ; Rees, astro-ph/ Tegmark et al. stressed that life may exist in universe with some of the cosmological parameters differing from those in our own universe by several orders of magnitude, if larger density fluctuations than those in our universe are allowed.

Graesser, Hsu, Jenkins and Wise, Phys. Lett. B600 (2004) Inflation model with potential of the inflaton We have Assume the distribution of the coupling constant be flat. The probability distribution of should be

The probability distribution for become After taking the variation of the amplitude of the primordial fluctuation into account, they found For R = 2 Mpc

VI. Anthropic principle favors holographic dark energy Q. G. Huang and M. Li, hep-th/ Since the holographic dark energy density evolves during the evolution of universe, we need to find the bound for it independently.

The bound on the holographic dark energy density at recombination is

The fraction of mass winding up in galaxies for the holographic dark energy model is

Normalized probability distribution The probability of a holographic dark energy with energy density greater than where

If we consider the variation of the amplitude of the primordial fluctuation

Our results

Our result shows that the anthropic principle makes a better prediction if dark energy is holographic.

Thank You!