Ricci Dark Energy Chao-Jun Feng SUCA, SHNU

Transcription

1 Ricci Dark Energy Chao-Jun Feng SUCA, SHNU

2 Outline n Introduction to Ricci Dark Energy (RDE) n Stability and the constraint on the parameter n Age problem alleviated in viscous version of RDE n Conclusion

3 Introduction n Dark Energy [

4 Equation of state Assuming: 68%CL : 95%CL : [arxiv: ]

5 Holographic Dark Energy(HDE) M. Li, Phys. Lett. B 603 (2004) 1, arxiv:hep-th/ C. Gao, X. Chen, Y.G. Shen, Phys. Rev. D 79 (2009) 04 n Holographic Principle: n HDE: Taking L as the future event horizon: n Results:

6 Ricci Dark Energy C. Gao, X. Chen, Y.G. Shen, Phys. Rev. D 79 (2009) , arxiv: [astro-ph]. Ricci Scalar The maximal black hole can be formed in the Universe is determined by the Casual Connection scale: R. G. Cai, B. Hu and Y. Zhang, Commun. Theor. Phys. 51,954(2009)[arXiv: [hep-th]]. For a flat Universe: R 2 CC = Ḣ + 2H2 ogical observation

7 n Solve the Friedmann equation: n Results:

8 Stability and Constraint Chao-Jun Feng and Xin-Zhou Li, Phys. Lett. B 680: , n Newtonian Gauge: ds 2 = (1 + 2Φ) dt 2 + a 2 (1 2Ψ )δ ij dx i dx j, [ ( n Perturbation Equations: 2 [ 3H 2 Φ 3H Φ + 2 where [ δρ R = α [ 2 δr = α 2 + = a 2 Φ a 2 Φ 3 Φ 15H Φ 6 ( Ḣ + 2H 2) Φ e[ δρ m denotes the perturbation ] of matter. E without matter: First, let us consider ] = δρ R + δρ m, denotes the perturbation of matter ] = + ( ],

9 Perturbation Equation in Fourier Mode n Without Matter ( ) [ n Solution Φ k (3 + 1 ) Φ k α (2 α) 3α k2 H 2 1 α 0 e 2( α )x Φ k = 0. [ ( ) ] w = 1 (ln ρ R) = 1 ( ) α 1, = and to make the universe accelerate [ ( ) ] [ Φ k = e 1 2 (3 α 1 )x( ( A k I ν kh 1 0 ξ) ( + B k K ν kh ξ)), where = ,, are modified Be ξ = 1 α α ( 2 α 3α )1/2 ( e (1 α) α x a ) ( + )) ( ( ) ν = 3α 1 /(2 2α), I ν, K ν are modified Bessel functions, B are integration constants, which should be determined

10 n If n If ) e initial c α > 1/3 ( Φ k (x ) B k e 1 2 (3 1 α )x 2 ν 1 Ɣ(ν) ( kh 1 ( ) [ ( ) ] α < 1/3, x = B k 2 ν 1 Ɣ(ν) ( kh 1 ( Φ k (x ) e (3 α 1 )x,.therefore,onlyif[ ( ) 1 3, bation will be a constant in the 0 ) ν [ 1 α α 0 ξ) ν ( 3α 2 α ) 1/2 ] ν, e initial c α > 1/3 n If α = 1/3, rturbation Stable k Φ k (x ) x. n is stable. We also plo Fitting: joint analysis in α = eoretically, which X. Zhang, arxiv:

11 Numerical Results

12 n With Matter: One can get the same results as that without matter n Numerical Results:

13 Viscous RDE C. J. Feng and X. Z. Li, Phys. Lett. B 680, 355(2009),arXiv: n Age parameter for LCDM: T (z) = z dz (1 + z )[Ω m0 (1 + z) 3 + (1 Ω m0 )] 1/2, hence, it easily satisfied the constraint t n Age for RDE Gyr, Fig. 2. The evolution of age of the universe in RDE model with α = 0.46 (solid), 0.76 (dashed), 1.0 (dot-dashed). Here h = 0.72 and Ω m0 = 0.27 are used. α < 1/3 will make the perturbation unstable, see [5].

14 Result for Viscous RDE Age problem is alleviated Fig. 3. The evolution of age of the universe in the viscous RDE model with α = 0.46 and τ m = 0 (solid), 0.03 (dashed), 0.06 (dot-dashed). Here h = 0.72 and Ω m0 = 0.27 are used.

15 Fig. 1. The total age of the universe in RDE model with respect to parameter α. Here h = 0.72 and Ω m0 = 0.20 (solid), 0.27 (dashed), 0.32 (dotted) are used. The horizontal shadow corresponds to the stellar age bound, namely t 0 = Gyr. [ ]

16 Conclusion n Viscosity seems a way to alleviate age problem! n What s dark energy? n Future observational results are required!

17 Thank you!