Transcript 幻灯片 1 - Nanyang Technological University

Dark Energy of the Universe
Xinmin Zhang
Institute of High Energy Physics, Beijing
Outline
1) Brief review on the dark energy models;
2) Current constraints on equation of state of dark energy
and the models;
3) 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:
4G
 / a  
a
3
(   3 p)
  0    3 p  0 w  p /   1 / 3
a
* Smoothly distributed, (almost ) not clustering
Candidates:
I Cosmological constant (or vacuum Energy)
T 

g 
8G
  p 
w  p /   1
 th /  ob ~ 10120

 ( 2  103 eV ) 4
8G

m ~ 10-3 eV
cosmological constant problem!
II Dynamical Field: Quintessence, Phantom, Quintom….
L
1
  Q  Q  V (Q )
2
Neutrino
Dark Energy?!
Q 
1 2
1 2
Q  V , pQ  Q
V
2
2

Models? V=?
Equation of state w=p/ρ:
* Vacuum :
* Quintessence:
* Phantom:
* Quintom:
characterize the properties of the dark energy models
w=-1
w  1
w<-1
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
  0  ,,  ,  
1  w  0, w
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
I.
Quintessence – like perturbation
II.
Phantom – like perturbation
III.
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
Constraints on dark energy with SN Ia + SDSS + WMAP1
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;
G. Zhao, H. Li, E. Linder,
K. Koyama, D. Bacon, XZhang
arXiV: 1109.1846 Sep
2011
with WMAP7+Union2.1+BAO+…
3）dynamical models are not
ruled out; quintom scenario
mildly favored；
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
Large Synoptic Survey
Telescope
BigBOSS
Euclid
G. Zhao, H. Zhan, Lifan
Wang, Z. Fan, X. Zhang,
arXiV: 1005.3810
Wide Field Infrared
Survey Telescope
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：
QF F 
• Mass varying neutrino：P.Gu, X.Wang and X.Zhang PRD68,
Q 
  p 

 ( 2  103 eV ) 4
8G

087301 (2003)
Rob Fardon, Ann E. Nelson, Neal Weiner JCAP 2004.
G.Dvali, Nature 432:567-568,2004
……
-3
m ~ 10 eV
* 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
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? 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)
I) Lint  c
nB 
 Q
M
b
J B
In thermo equilibrium

Cohen & Kaplan
gb
 nb 
2 2


m
1/ 2
E(E  m )
2
T 2
g bT 3 b
b 3
g bQ

[
 O(
) ]c
6
T
T
6M
2
dE  [ 1 exp[( E1 b ) / T ]  1 exp[( E1 b ) / T ] ]

15c g bQ
  nB / s 
4 2 g MT
: 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)
Leptogenesis
Anomaly
for CMB
Testing CPT symmetry with CMB polarizations
i: source
f: observer
CPT violation
predicting <TB> and <EB>
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)
Current status on the
measurements of the
rotation angle
===
PLANCK :   0.057 deg
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-RoberstonWalker 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
Action:
Potential:
1
1

S   d x  g [  1 1   2 2  V (1 , 2 )]
2
2
4
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.
Basically 5 kinds of Galileon model:
But can be generalized…
C. Deffayet et al., Phys.Rev.D79:084003,2009.
A. Nicolis et al., Phys.Rev.D79:064036,2009;
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：
At the bouncing point:

20
H  0；
Expanding
Phase:
H  0.
18
16
14
H 0
Around it:

H  0.
H  4G (   p )  w  1
12
a108
6
4
2
a=1
Transition to the observable universe w  1.
0
-10 -8 -6 -4 -2 0
2
(radiation dominant, matter dominant,…)
So w needs to cross -1, and
t
Quintom matter is required！Y. Cai, T. Qiu, Y. Piao, Mi. Li, X. Zhang, JHEP 0710:071,2007.
4
6
8
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.
10
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
！