Quintom CosmologyTao-Tao Qiu & Yi-Fu Cai, IHEP

2008-09-21

OutlineIA Brief Review on Quintom ModelsTheoretical challenge to the Quintom Model-building: No-Go TheoremExamples of Quintom modelsIIApplication of Quintom Models in Early Universe: Quintom BounceBasic idea of Quintom bounceExamples of Quintom bounceMore on Quintom bounce scenario: perturbation (III) Extension of Quintom Bounce: Cyclic Scenario of the Universe (IV) Conclusions and Outlook

Dark Energy: A mysterious Force Driving the Acceleration of the Universe Einstein Equation Negative pressure; Not (almost) clustering; IA Brief Review on Quintom ModelsQuintom CosmologyFeatures:Metric:Beginning From Data(i-i) component - (0-0) component:

Challenge: Data favors that w crosses -1 !Candidates for DE

Cosmological Constant w=-1;

Quintessence w>-1;

III. Phantom w-1 or w

Theoretical interpretation: No-Go TheoremFor 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/0703202Theoretical challenge to the Quintom Model-buildingQuintom CosmologyIA Brief Review on Quintom Models

Solutions: Various Quintom ModelsQuintom CosmologyConditions 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-derivativePossible 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)

IA Brief Review on Quintom Models

Double Field ModelBo 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 ModelsQuintom Cosmology

Single Scalar Field with High DerivativeQuintom CosmologyThe simplest action:I A Brief Review on Quintom Models Examples of Quintom ModelsMore complicated:I. Arefeva and A. Koshelev, JHEP 0702:041,2007.

String-inspired Quintom ModelActionDifferent 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 CosmologyI A Brief Review on Quintom Models Examples of Quintom Models

Background(Equation of State)w crosses -1Perturbation (sound speedsquared)The model with different potentialsQuintom CosmologyI A Brief Review on Quintom Models Examples of Quintom Models0<

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

The dilemma of Big Bang Cosmology Though widely recognized, there are still problems existing in Big Bang Cosmology:

Singularity ProblemFlatness ProblemHomogeneity ProblemLarge Scale StructureUnwanted Relics

Inflationary Cosmology can solve most of these problems, but singularity still remains a problem.IIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)Quintom Cosmology

Basic idea of Quintom BounceThe 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 phaseExpandingPhase:At the boun-cing point:Around it:Transition to the observable universe (ra-diation dominant, matter dominant,) w>-1So w needs to cross -1, and Quintom is re-quiredY. Cai, T. Qiu, Y. Piao, M. Li and X. Zhang, JHEP 0710:071, 2007IIApplication of Quintom Models inBouncing Cosmology (Quintom Bounce)Quintom Cosmology

A phenomenological Quintom model with the equation of state across -1 can lead to a bouncing solution.I. Quintom Bounce with Parameterized EoSQuintom CosmologyIIApplication of Quintom Models inBouncing Cosmology (Quintom Bounce)

II. Quintom Bounce with Double FieldsThe actionwhereQuintom CosmologyIIApplication of Quintom Models inBouncing Cosmology (Quintom Bounce)

III. Quintom Bounce with a single scalar fieldThe action:whereQuintom CosmologyIIApplication of Quintom Models inBouncing Cosmology (Quintom Bounce)

The action:Y. Cai and T. Qiu, R. Brandenberger, Y. Piao and X. Zhang, JCAP 0803:013, 2008IIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)Quintom CosmologyDetecting 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.

Quintom CosmologyThe sketch plot of the perturbation modesFor field perturbation:IIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)

The Calculation of the perturbations on Quintom BouncePerturbed metric:Perturbation equations:(I) For metric:(II) For fields:Quintom CosmologyIIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)

The Analytical Results of CalculationBy 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 CosmologyIIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)Super-horizonSub-horizon

The Numerical Results of CalculationQuintom CosmologyIIApplication of Quintom Models in Bouncing Cosmology (Quintom Bounce)

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

Extension of bouncing: Cyclic UniverseQuintom Cosmology Basic Motivation: 1) Avoid the Problem of Singularity 2) Avoid the Problem of CoincidenceTwo 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.IIIExtension of Bouncing Cosmology:Cyclic Universe with Quintom Matter

Quintom CosmologyConcrete ExampleEinstein Equation:with the Lagrangian:The solutions can be divided into five cases: ( is related to initial condition)Case I:Case II:IIIExtension of Bouncing Cosmology:Cyclic Universe with Quintom Matter

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

Other Models to avoid SingularityPre-big bang Scenario (G. Veneziano et al.)Cyclic model Ekpyrotic modelBouncing 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 CosmologyOur model is based on 4D Einstein Gravity!!!Similar to:Difference: New Ekpyrotic model (E. Buchbinder et al.) K-Bounce (L. Abramo et al.)

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 perturbationAn extension: Cyclic Universe with Quintom matter

IVConclusions and OutlookQuintom Cosmology

Thank you!!!

***