Dark Energy of the Universe Xinmin Zhang Institute of High Energy Physics, Beijing Outline Brief review on the dark energy models; Current constraints on equation of state of dark energy and the models; Interacting dark energy: i) Neutrino dark energy (mass varying neutrino) LV varying neutrino: “OPERA and Neutrino DE model” Ciuffoli, Evslin, Liu and Zhang, arXiv: 1109.6641 ii) Quintessential Baryo/Leptogenesis ( cosmological CPT violation) iii Testing CPT symmetry with CMB polarization 4) Quintom cosmology: Quintom model buildings, quintom bounce 5) Summary

Brief Introduction to Dark Energy Negative pressure:  * Smoothly distributed, (almost ) not clustering Candidates: I Cosmological constant (or vacuum Energy) Neutrino Dark Energy?! cosmological constant problem! II Dynamical Field: Quintessence, Phantom, Quintom….  Models? V=?

Equation of state w=p/ρ: characterize the properties of the dark energy models * Vacuum : w=-1 * Quintessence: * Phantom: w<-1 * Quintom: w across -1 Crucial Important: determining the equation of state of dark energy with experiments (cosmological observations) Parameterization of the equation of state: (very much like S.T.U parameters introduced for the precision measurements of the standard model ) i) w=w_0+w_1 z (for small z) ii) w=w_0+w_1 z / (1+z) ===== (used mostly in the literature) iii) w=w_0+w_1 sin(w_2 ln(a)+w_3)

General parameters of cosmological models: Global analysis with current astronomical observational data: SN (Union2.1, SNLS3) LSS (SDSS), CMB(WMAP7, …) And code used CAMB/CosmoMC However, difficulty with the dark energy perturbation when w across -1 ========== divergent δ, θ: density perturbation and the divergence of the fluid velocity respectively

Perturbation of DE is continuous during crossing! Perturbation with Quintom scenario of dark energy (introducing extra degrees of freedom such as 2-scalar field, 1-scalar with higher derivatives…… ) Perturbation of DE is continuous during crossing! Feng, Wang, Zhang, Phys. Lett. B607, 35 (2005) Zhao et.al., Phys.Rev.D 72,123515, (2005) Y. Cai et. al., Phys Rept. 493:1-60, (2010)

Our strategy to handle perturbations when w crosses -1 Quintessence – like perturbation Phantom – like perturbation Quintom-based perturbation Zhao et.al Phys.Rev.D 72,123515, 2005 M. Li, Y. Cai, H. Li, R. Brandenberger, X. Zhang, e-Print: arXiv:1008.1684  Similarly, W. Fang, Wayne Hu, Lewis Phys.Rev.D78:087303, 2008

Observing dark energy dynamics with supernova, microwave background Constraints on dark energy with SN Ia + SDSS + WMAP-1 Observing dark energy dynamics with supernova, microwave background and galaxy clustering Jun-Qing Xia, Gong-Bo Zhao, Bo Feng, Hong Li and Xinmin Zhang Phys.Rev.D73, 063521, 2006 = Dark energy perturbation: theoretically consistence required; numerically important!

Current status in determining the EoS of dark energy G. Zhao and X. Zhang Phys.Rev.D81:043518,2010 WMAP7 E. Komatsu et al. e-Print: arXiv:1001.4538 SNLS3， e-Print: arXiv:1104.1444  Results: 1) Current data has constrained a lot of the theoretical models; 2) Cosmological constant is consistent with the data; 3）dynamical models are not ruled out; quintom scenario mildly favored； G. Zhao, H. Li, E. Linder, K. Koyama, D. Bacon, XZhang arXiV: 1109.1846 Sep 2011 with WMAP7+Union2.1+BAO+…

Understanding the nature of accelerating universe is a big challenge to particle physics Current status 1) on constraints on EoS of dark energy (w_0, w_a) O(10%) future projects: w at level of O(1%), 2) on modified gravity a) GR works well; b) Background evolution: Quintom behaviour “Testing Einstein Gravity with Cosmic Growth and Expansion” Gongbo Zhao, Hong Li, Eric Linder, Kazuya Koyama, David Bacon, Xinmin Zhang, arXiv: 1109.1846, Sept, (2011) with SN(Union2.1)+CMB(WMAP7) +WL(CFHTLS) + BAO + PV

Future Projects on Dark Energy Study KDUST: Kunlun Dark Universe Telescope G. Zhao, H. Zhan, Lifan Wang, Z. Fan, X. Zhang, arXiV: 1005.3810 Wide Field Infrared Survey Telescope Large Synoptic Survey Telescope Euclid BigBOSS 10

Cosmological Constant? Or Dynamical Dark Energy 预言宇宙演化的不同行为

Interacting Dark Energy ----non-gravitational method Coupling constant vary： Mass varying neutrino：P.Gu, X.Wang and X.Zhang PRD68, 087301 (2003) Rob Fardon, Ann E. Nelson, Neal Weiner JCAP 2004. G.Dvali, Nature 432:567-568,2004    ……  * Correlations between EoS of DE and neutrino mass --------- neutrino mass limit relaxed by factor 2 H. Li et al

Neutrino Dark Energy and Lorentz & CPT violation

Opera and a neutrino dark energy model Emilio Ciuffoli, Jarah Evslin, Jie Liu and Xinmin Zhang ArXiv: 1109.6641

CPT violation when rolling down Interacting Dark Energy with derivatives couplings * Direct coupling with ordinary matter strongly constrained by the long-range force limits large radiative corrections to the DE potential * Interaction with derivative Goldstone theorem: Spin-dependent force CPT violation when rolling down Baryo/Leptogenesis in thermo equilibrium Quintessential Baryo/Leptogenesis Anomaly Equation CMB polarization and CPT test Cosmological CPT violation: strength ~ O( H ), unobservable in the laborary experiments CMB: travelling around O(1/H), so accumulated effect ~ O(1) observable !

Baryogenesis Andrei Sakharov （1967年） 三个条件： i) B violation ----GUT theory ii) C and CP violation -----K, B system … iii)Out of thermo-equilibrium (CPT conserved) Freezing out of the heavy particles If CPT is broken, can be generated in thermo-equilibrium

Electroweak Baryogenesis i) B violation ----anomaly, non-trivial vacuum, sphaleron ii) C and CP violation -----CKM mechanism (however, too small-new physics) iii) First order phase transition Need Higgs mass < 40 GeV! Need New physics

Effective lagrangian approaches to EW baryogenesis 1) Higher dimensional operator relevant to Higgs mass limit Effective potential:

== Xinmin Zhang PRD47, 3065 (1993) Cedric Delaunay, Christophe Grojean, James D. Wells JHEP 0804:029,2008 Electroweak vacuum stability A. Datta, B.-L. Young and X. Zhang PLB385, 225 (1996) Prediction for a light Higgs !

2) Operator relevant to baryon number generation (Why top 2) Operator relevant to baryon number generation (Why top? Interacting strongly with the bubble wall ) === ===== Anomalous top-Higgs couplings: X. Zhang et al, PRD 50, 7042 (1994) Lars Fromme, Stephan J. Huber, JHEP 0703:049,2007

Electroweak baryogenesis and anomalous Top, Higgs coups == = Probing for anomalous Top, Higgs couplings at Tevatron, LHC, ILC…

Leptogenesis Taking into account the gauge interaction, Yukawa interaction and also QCD sphaleron

Quintessential Baryo/Leptogenesis M.Li, X.Wang, B.Feng, X. Zhang PRD65,103511 (2002) De Felice, Nasri, Trodden, PRD67:043509(2003) M.Li & X. Zhang, PLB573,20 (2003) In thermo equilibrium I)  Cohen & Kaplan : depends on the model of Quintessence II) Cosmological CPT violation, baryo/leptogenesis and CMB polarization M. Li, J. Xia, H. Li and X. Zhang Phys. Lett. B651, 357 (2007) Anomaly for CMB Leptogenesis

Testing CPT symmetry with CMB polarizations i: source f: observer Bo Feng, Hong Li, Mingzhe Li and Xinmin Zhang Phys. Lett. B 620, 27 (2005); Bo Feng, Mingzhe Li , Jun-Qing Xia, Xuelei Chen and Xinmin Zhang Phys. Rev. Lett. 96, 221302 (2006) CPT violation predicting <TB> and <EB>

Current status on the measurements of the rotation angle === 26

More On CPT test with CMB * Feature: CMB photon travelling over the distance around the observed universe, provides the most sensitive test to CPT ** Rotation angle: a cosmological parameter needed be measured by CMB *** Sources of the CMB polarization for the B-mode: i)Tensor perturbation; i i)CPT violating effect; iii)Lensing **** Spatial dependent rotation angle: DE scalar fluctuation Anomalous axion string effect (?)

Discussions on theoretical DE models * cosmological constant problem ** Consistent DE and modified gravity models *** quintom cosmology (For a review, see, Yifu Cai et al, Phys.Rept. 493:1-60, (2010); T. Qiu, Mod.Phys.Lett.A25:909-921,2010). Current data show: EoS of dark energy and effective EoS of modified gravity mildly favored==quintom with w crosses over w=-1 during the evolution Why interested these years theoretically? 1) Challenges to the model buildings theoretically interesting! (no-go theorem) 2) Quintom bouncing cosmology standard cosmology-singular quintom cosmology-non-singular

NO-GO Theorem For theory of dark energy in the 4D Friedmann-Roberston-Walker universe described by a single perfect fluid(1) or a single scalar field with a lagrangian of (2), which minimally (3) couples to Einstein Gravity (4), its equation of state cannot cross over the cosmological constant boundary. Feng, Wang & Zhang, Phys. Lett. B 607:35, 2005, astro-ph/0404224 ; Vikman, Phys. Rev. D 71:023515, 2005, astro-ph/0407107 ; Hu, Phys. Rev. D 71:047301, 2005; Caldwell & Doran, Phys. Rev. D 72:043527, 2005; Zhao, Xia, Li, Feng & Zhang, Phys. Rev. D 72:123515, 2005; Kunz & Sapone, Phys. Rev. D 74:123503, 2006; …… Xia, CYF, Qiu, Zhao, & Zhang, Int.J.Mod.Phys.D17:1229,2008 To realize Quintom, one of the conditions should be violated

Quintom Model I: Double-field Potential: Action: Benefits: w can cross -1; Easily fit to observations; With specific potentials it has tracking behavior; Classical perturbations are well defined. Problem: If quantized, it is unstable because of a ghost. Feng, Wang & Zhang, PLB 607:35, 2005; Guo, Piao, Zhang & Zhang, PLB608:177,2005

Quintom Model II: a single scalar with higher derivatives Lagrangian: Equivalent Lagrangian: where we have redefine, Progress: Perturbatively well-defined; Problem: Incomplete in ultraviolet limit. Li, Feng & Zhang, JCAP 0512:002,2005; Zhang & Qiu, PLB642:187-191,2006

Quintom Model III: Spinor Quintom Action: The vierbein algebra yields: Progresses: No ghost; With certain potential, it has the similar behavior of Chaplygin gas, namely Weak point: An effectively negative mass when w is below -1. CYF & Wang, CQG25:165014,2008

Quintom examples in string theory Descriptions: A rolling tachyon is effectively described by a non-local cubic string field theory, which corresponds to a slowly decaying D3-brane; In a local approximation, this model contains quintom degrees of freedom. The model: where At low energy limit, it behaves as a double-field quintom; Aref'eva, Koshelev & Vernov, PRD72:064017,2005 While at high energy scale, the model contains multiple quintom degrees of freedom. Mulryne & Nunes, PRD78:063519,2008

Quintom examples in string theory An equivalent scenario with a generalized DBI action: with the potential: This is an action including higher derivatives, but of a non-perturbative form. (beta term involves two scalars and two derivatives, the same as alpha term) The quantization of this class of models is still an open issue. CYF, Li, Lu, Piao, Qiu & Zhang, PLB651:1,2007

Galileon Theories Galileon Models: Lagrangian with higher derivative operator, but the equation of motion remains second order, so the model can have w cross -1 without ghost mode. C. Deffayet et al., Phys.Rev.D79:084003,2009. Nicolis et al., Phys.Rev.D79:064036,2009; Basically 5 kinds of Galileon model: But can be generalized… C. Deffayet et al., arXiv:1103.3260 [hep-th]

An example of Galileon Theory The action: which was also used in arXiv: 1007.0027 for “Galileon Genesis”. Stress energy tensor: From which we get energy density and pressure: where

Quintom Bounce The expanding of the universe is transited from a contracting phase; during the transition the scale factor of the universe a 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 (radiation dominant, matter dominant,…) So w needs to cross -1, and Quintom matter is required！ Y. Cai, T. Qiu, Y. Piao, Mi. Li, X. Zhang, JHEP 0710:071,2007.  Y. Cai, T. Qiu, R. Brandenberger, Y. Piao, X. Zhang, JCAP 0803:013,2008.  Y. Cai, T. Qiu, R. Brandenberger, X. Zhang, Phys.Rev.D80:023511,2009. 

Ekpyrotic Model The collision of two M branes in 5D gives rise to a nonsingular cyclic universe, and the description of effective field theory in 4D is 1 DE domination 2 decelerated expansion 3 turnaround 4 ekpyrotic contracting phase 5 before big crunch 6 a singular bounce in 4D 7 after big bang 8 radiation domination 9 matter domination Failure of effective field theory description, uncertainty involved in perturbations.

Examples: 1 Two Field Quintom

Examples: 1 A single scalar with high-derivative term

Oscillating universe with Quintom matter H. Xiong, Y. Cai, T. Qiu, Y. Piao, X. Zhang, PLB666:212-217,2008.  Solution:

Summary I) Current status in understanding the physics of accelerating Universe DE: Cosmological constant: well fit; however best fit: Quintom MG: GR + “effective (quintom) DE” =====Quintom dark energy theory ====quintom bounce ===QUINTOM cosmology Interesting Correspondence: Inflation =Quintessence Bounce  Quintom II) Interacting Dark Energy ==== Lorentz & CPT violation Implications for neutrino (neutrino superluminal) Baryo/leptogenesis CMB polarization

Thank you ! 新年快乐！