1. Quintom Cosmology Tao-Tao Qiu & Yi-Fu Cai, IHEP （邱涛涛、蔡一夫， 中科院高能所） 2008-09-21 （ “ 精灵 ” 宇宙学）

2. Outline （ I ） A Brief Review on Quintom Models Theoretical challenge to the Quintom Model-building: No-Go Theorem Examples of Quintom models （ II ） Application of Quintom Models in Early Universe: Quintom Bounce Basic idea of Quintom bounce Examples of Quintom bounce More on Quintom bounce scenario: perturbation (III) Extension of Quintom Bounce: Cyclic Scenario of the Universe (IV) Conclusions and Outlook

3. Dark Energy: A mysterious Force Driving the Acceleration of the Universe Einstein Equation ： Negative pressure; Not (almost) clustering; … （ I ） A Brief Review on Quintom Models Quintom Cosmology Features: Metric: Beginning From Data (i-i) component - (0-0) component:

4. Challenge: Data favors that w crosses -1 ! Candidates for DE ： I.Cosmological Constant w=-1; II.Quintessence w>-1; III. Phantom w<-1; IV.K-essence w>-1 or w<-1; V. Quintom w crosses -1; … Quintom Cosmology J. Q. Xia, H. Li, G. B. Zhao and X. M. Zhang, arXiv:0807.3878 [astro-ph] （ I ） A Brief Review on Quintom Models Beginning From Data

5. Theoretical interpretation: No-Go Theorem For theory of dark energy (DE) in the 4D Friedmann- Robertson-Walker (FRW) universe described by a single perfect fluid or a single scalar field with a lagrangian of, which minimally couples to Einstein Gravity, its equation of state w cannot cross over the cosmological constant boundary. Bo Feng et al., Phys. Lett. B 607, 35 (2005); A. Vikman, Phys. Rev. D 71, 023515 (2005); W. Hu, Phys. Rev. D 71, 047301 (2005); R. R. Caldwell and M. Doran, Phys. Rev. D 72, 043527 (2005); Gong-Bo Zhao et al., Phys. Rev. D 72, 123515 (2005); H. Wei, PhD Thesis (2006); M. Kunz and D. Sapone, Phys. Rev. D 74, 123503 (2006); …… J. Xia, Y. F. Cai, T. Qiu, G. B. Zhao and X. M. Zhang, astro-ph/0703202 Theoretical challenge to the Quintom Model-building Quintom Cosmology （ I ） A Brief Review on Quintom Models

6. Solutions: Various Quintom Models Quintom Cosmology Conditions needed to be broken to make w cross -1: 1. 4D space-time 2. Einstein Gravity with FRW metric 3. single component 4. scalar field 5. no higher-derivative Possible quintom models: 1.two scalar field (Bo Feng et al., astro-ph/0404224, etc) 2. single scalar field with higher derivative (M. Z. Li et al., hep-ph/0503268, I. Arefeva et al., hep-th/0605085 etc) 3. including vector or spinor field (C. A. Picon, astro-ph/0405267, Y. Cai and J. Wang, arXiv:0806.3890 [hep-th], etc) 4. non-minimal coupling or modified gravity (L. Perivolaropoulos, astro-ph/0504582, S. Nojiri et al., hep-th/0504052, etc) 5. braneworld models (R. G. Cai et al., hep-th/0505186, etc) …… （ I ） A Brief Review on Quintom Models

7. Double Field Model Bo Feng, Xiulian Wang and Xinmin Zhang, Phys. Lett. B 607, 35 (2005) Action: Potential:  w can cross -1 easily! （ I ） A Brief Review on Quintom Models Examples of Quintom Models Quintom Cosmology

8. Single Scalar Field with High Derivative Quintom Cosmology The simplest action: （ I ） A Brief Review on Quintom Models Examples of Quintom Models More complicated: I. Aref’eva and A. Koshelev, JHEP 0702:041,2007.

9. String-inspired Quintom Model Action ： Different from conventional single scalar field with high derivative, this Quintom model (beta term involves two scalars and two derivatives, the same as alpha term) has its HD term residing in the square root. This model can be viewed as a generalization of tachyon models. Potential: Y. Cai, M. Li, J. Lu, Y. Piao, T. Qiu and X. M. Zhang, Phys. Lett. B 651, 1 (2007) Quintom Cosmology （ I ） A Brief Review on Quintom Models Examples of Quintom Models

10. Background (Equation of State) w crosses -1 Perturbation (sound speed squared) The model with different potentials Quintom Cosmology （ I ） A Brief Review on Quintom Models Examples of Quintom Models 0< <1

11. Vector field: Quintom Cosmology Other Candidates for Dark Energy with w crossing -1 Modified Gravity: Higher Dimensional works: R. Cai et al., Commun.Theor.Phys.44:948,2005 C. Picon, JCAP 0407:007,2004 L. Perivolaropoulos, JCAP 0510:001,2005 （ I ） A Brief Review on Quintom Models Examples of Quintom Models

12. The dilemma of Big Bang Cosmology Though widely recognized, there are still problems existing in Big Bang Cosmology:  Singularity Problem  Flatness Problem  Homogeneity Problem  Large Scale Structure  Unwanted Relics  。。。。。。 Inflationary Cosmology can solve most of these problems, but singularity still remains a problem. （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce) Quintom Cosmology

13. Basic idea of Quintom Bounce The expanding of the universe is transited from a contracting phase; during the transition the scale factor of the universe is at its minimum but non-vanishing, thus the singularity problem can be avoided. Contracting phase ： Expanding Phase: At the boun- cing point: Around it: Transition to the observable universe (ra- diation dominant, matter dominant,…) w>-1 So w needs to cross -1, and Quintom is re- quired ！ Y. Cai, T. Qiu, Y. Piao, M. Li and X. Zhang, JHEP 0710:071, 2007 （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce) Quintom Cosmology

14. A phenomenological Quintom model with the equation of state across -1 can lead to a bouncing solution. I. Quintom Bounce with Parameterized EoS Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

15. II. Quintom Bounce with Double Fields The action ： where Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

16. III. Quintom Bounce with a single scalar field The action: where Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

17. The action: Y. Cai and T. Qiu, R. Brandenberger, Y. Piao and X. Zhang, JCAP 0803:013, 2008 （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce) Quintom Cosmology Detecting the Signature of Bouncing Model: Working with an Example Y. Cai and T. Qiu et al., arXiv:0808.0819 [astro-ph] and present normal and ghost field respectively, with V only the function of. We can choose V to have slow-rolling after the bounce. At some time during evolution the ghost will dominate the universe, making its EOS (w) less than -1 which lead to bounce; after bounce the kinetic term of dilutes as, making slow-rolling field dominate again, thus inflation emerges.

18. Quintom Cosmology The sketch plot of the perturbation modes For field perturbation: （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

19. The Calculation of the perturbations on Quintom Bounce Perturbed metric: Perturbation equations: (I) For metric: (II) For fields: Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

20. The Analytical Results of Calculation By solving these equations, we got: (I) In heating phase: (II) In slow-climb-contracting phase: (III) In bouncing phase: (IV) In slow-roll-expanding phase: Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce) Super-horizonSub-horizon

21. The Numerical Results of Calculation Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce)

22. Quintom Cosmology （ II ） Application of Quintom Models in Bouncing Cosmology (Quintom Bounce) Comparing to the Observational Data Y. Cai and T. Qiu et al., arXiv:0808.0819 [astro-ph]

23. Extension of bouncing: Cyclic Universe Quintom Cosmology Basic Motivation: 1) Avoid the Problem of Singularity 2) Avoid the Problem of Coincidence Two definitions: 1) Universe with cyclic Hubble Parameter but always expanding; 2) Universe with cyclic scale factor which contracts and expands alternately. B. Feng, M. Li, Y. Piao and X. M. Zhang, Phys.Lett.B634:101-105,2006. （ III ） Extension of Bouncing Cosmology: Cyclic Universe with Quintom Matter

24. Quintom Cosmology Concrete Example Einstein Equation: with the Lagrangian: The solutions can be divided into five cases: ( is related to initial condition) Case I:Case II: （ III ） Extension of Bouncing Cosmology: Cyclic Universe with Quintom Matter

25. Quintom Cosmology Case III:Case IV: Case V: H. Xiong, Y. Cai, T. Qiu, Y. Piao and X. M. Zhang, Phys.Lett.B666:212-217,2008. （ III ） Extension of Bouncing Cosmology: Cyclic Universe with Quintom Matter This case corresponds to a contracting universe for ever and has been excluded by the astronomical observations.

26. Other Models to avoid Singularity  Pre-big bang Scenario (G. Veneziano et al.)  Cyclic model  Ekpyrotic model  Bouncing in Modified Gravity (A. Mazumdar et al.)  Bouncing Brane model (R. Brandenberger et al.) (P. Steinhardt et al.) Other Than (II) and (III): Maybe There is Something More … Quintom Cosmology Our model is based on 4D Einstein Gravity!!! Similar to: Difference: New Ekpyrotic model (E. Buchbinder et al.) K-Bounce (L. Abramo et al.)

27. Conclusions and Outlook Quintom Dark Energy is favored mildly by the current data. Theoretically Quintom model building is a challenge. Interesting application of Quintom matter:  in early universe: Quintom Bounce and its perturbation  An extension: Cyclic Universe with Quintom matter （ IV ） Conclusions and Outlook Quintom Cosmology

28. Thank you!!!