2. Theoretical Aspects of Dark Energy Models Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences CCAST, July 4, 2005

3. Cosmic Acceleration? Dynamics equations: (Violate the Strong Energy Condition: exotic energy component)

4. Dark Energy? Observation Data Theoretical Assumptions General RelativityCosmo Principle Model IModel II Model III

5. Model I: Modifications of Gravitational Theory 1) GR’s test UV: ~ 1 mm IR: ~ solar scale 2) Modify GR UV: quantum gravity effect IR: cosmos scale Brane World Scenario

6. Modifying GR in IR: 1)“ Ghost Condensation and a Consistent Infrared Modification of Gravity” by N. arkani-Hamed et al, hep-th/0312099,JHEP 0405 (2004) 074.

7. Consider a ghost field with a wrong-sign kinetic term:

8. Suppose the scalar field has a constant velocity: The low-energy effective action for the fluctuation has an usual form:

9. 2) “ Is Cosmic Speed-up due to New Gravitational Physics ” by S. M. Carroll et al. astro-ph/0306438, Phys.Rev. D70 (2004) 043528 Consider a modification becoming important at extremely low curvature

10. Making a conformal transformation yields a scalar field with potential: (1) Eternal de Sitter; (2) power-law acceleration; (3) future singularity

11. General case:

12. More general case: hep-th/0410031, PR D71:063513,2005 Consider:

13. 3) Brane World Scenario: y 1) N. Arkani-Hamed et al, 1998 factorizable product 2) L. Randall and R. Sundrum, 1999 warped product in AdS_5 RS1: RS2: 3) DGP model, 2000 a brane embedded in a Minkovski space

14. a) A popular model: RS scenario where = 0 Fine-Tuning

15. 2) “Dark Energy” on the brane world scenario “Braneworld models of dark energy” by V. Sahni and Y. Shtanov, astro-ph/0202346, JCAP 0311 (2003) 014 When m=0:

16. In general they have two branches:

19. Current value of the effective equation of state of “dark energy”

20. The acceleration can be a transient phenomenon: Brane 2

21. However, w crosses –1, the phantom divide? D. Huterer and A. Cooray, astro-ph/040462; Phys.Rev. D71 (2005) 023506

22. “Crossing w=-1 in Gauss-Bonnet Brane World with Induced Gravity ” by R.G. Cai,H.S. Zhang and A. Wang, hep-th/0505186 Consider the model

23. The equations of motion:

24. The effective equation of state of “dark energy”: Where the Gauss-Bonnet term in the bulk and bulk mass play a curial role.

25. Model III: Back Reaction of Fluctuations “Cosmological influence of super-Hubble perturbations” by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, astro-ph/0410541; “Primordial inflation explains why the universe is accelerating today” by E.W. Kolb, S. Matarrese, A. Notari and A. Riotto, hep-th//0503117; “On cosmic acceleration without dark energy” by E.W. Kolb, S. Matarrese, and A. Riotto, astro-ph/0506534

26. Inflation produces super-horizon perturbations!

27. Consider the presence of cosmic perturbations, Split the gravitational potential to two parts

28. A local observer within the Hubble volume will see cosmological constant

29. which indicates the SHCDM with is indistinguishable from LCDM model.

30. Another scenario:

31. Beyond the super-horizon mode’s cut-off, the bulk universe is There is a super-horizon sized underdense bubble containing the observable universe, with matter density equal to the average matter density we measure locally

33. Model II: Various Dark Energy Models: Acts as Source of E’eq (1)Cosmological constant: w=-1 (2) Holographic energy (3) Quintessence: -1<w<0 (4) K-essence: -1 <w<0 (5) Chaplygin gas: p=- A/rho (6) Phantom: w<-1 (7) Quintom (8) Chameleon, K-Chameleon various generalization and mixture……..

34. QFT, a very successful theory (1) a very tiny positive cosmological constant ? Variable cosmological constant? Interaction?

35. (2) Holographic Energy? E,S V,A R i) Bekenstein Bound: ii) Holographic Bound: iii) UV/IR Mixture: (Cohen et al, Hsu, Li….)

36. (3) Quintessence: a very slowly varying scalar field? Tracker Potential: (4) K-essence (Born-Infeld Scalar Field):

37. (5) Chaplygin gas ? Generalizations:

38. (6) Phantom (Caldwell, 1999) -1<w<0, if s=1 w<-1, if s=-1

39. (7) Quintom: normal scalar field plus phantom field W cross the phantom divide, w=-1 (8) Chameleon, K-Chameleon Hessence ?

40. Acceleration Deceleration Distance between galaxies Time (Age of universe) Beginning Now (13.7 billion years) Inflation (acceleration) Closed, rho<0 Acc.(-1 <w<-1/3) Super Acc. (w<-1) ? Expand, but w>0 The fate of our universe depends on the nature of dark energy, not only the geometry Radiation + dust) (dark energy dominated)

41. Thanks!