Dark Energy, Cosmological CPT
Violation and Baryo/Leptogenesis
Xinmin Zhang
Institute of high energy physics
Outline
1) Brief review on the dark energy study;
2) Interacting dark energy and cosmological CPT violation:
3) Baryo/Leptogenesis and CMB polarization
4) Quintessino dark matter
Lorentz and CPT violation:
Theory: models and speculations;
Evidence: none in particle physics experiments
cosmology, expanding universe
no antimatter (CPT violation or not)
Interacting Dark Energy
====Quintessential Baryo/Leptogenesis (cosmological CPT violation)
======== Axion-like coupling Q F_\mu\nu \tilde F^\munu
===== CMB polarization = Susying, Quintessino (DM)
a model for dark energy, dark matter and baryon matter
Negative pressure:
 / a  
a
4 G
Dark Energy:
(  3 p)
3
  0    3 p  0
a
w  p /   1 / 3
* Smoothly distributed, (almost ) not clustering
Candidates:
I Cosmological constant (or vacuum Energy)
T 


8 G
g

cosmological constant problem!
w  p /   1
 th / 
ob
~ 10
120
II Dynamical Field: Quintessence, Phantom, Quintom….
L 
1
2

  Q  Q  V (Q )
Q 
1 2
1 2
Q  V , pQ 
Q V
2
2
 1  wQ  1
Equation of state w=p/ρ: characterize the properties of the dark energy models
* Vacuum :
* Quintessence:
w=-1
w  1
* Phantom: w<-1
* Quintom: w across -1
Important determining the equation of state of dark energy
with cosmological observations
I) Parameterization of equation of state:
A) w=w_0+w_1 z (for small z)
B) w=w_0+w_1 z / (1+z) (used mostly in the literature)
C) w=w_0+w_1 sin(w_2 ln(a)+w_3)
Cosmological
Parameters:
II) Global analysis with
II)
current astronomical
observational data:
SN (Union2.1, SNLS3)
LSS (SDSS),
CMB(WMAP, …)
And
CAMB/CosmoMC
However, difficulty with the dark energy perturbation
when w across -1 ========== divergent
1  w  0 , w  0   ,  ,  ,   
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.
Examples of Quintom models:
1) Two scalar fields:
2) Single scalar with high derivatives:
3) Modified Born-Infeld action:
V0
V ( ) 
e
 
e

,
Perturbation with Quintom dark energy
Here δ and θ are the density perturbation and the divergence of the
fluid velocity respectively
Perturbation of DE is continuous during crossing!
Zhao et.al Phys.Rev.D 72,123515,2005
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
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
Current status in determining the EoS of
dark energy
Gongbo Zhao and Xinmin Zhang
Phys.Rev.D81:043518,2010
SNLS3，
e-Print:
arXiv:1104.1444
WMAP7 E. Komatsu et al.
e-Print: arXiv:1001.4538
1) Current data has constrained
a lot of the models;
2) Cosmological constant is
consistent with the data;
3）dynamical models are not ruled
out; quintom mildly favored；
4) Need more data to get w_0, w_a with
error around O(1 %).
Interacting Dark Energy
(Quintessence …)
*
Direct coupling with ordinary matter
strongly constrained by the long-range force limits
*
Interaction with derivative
Goldstone theorem: Spin-dependent force
== cosmological CPT violation,
a unified model of DE and Baryo(Lepto)genesis:
Quintessential Baryo/Leptogenesis
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)
L int  c
 Q
M
nB 

g bT
6
b
3
[
In thermo equilibrium

Cohen & Kaplan
 nb 
b
T

JB
 O(
gb
2
b
2

E (E
2
m )
2
m
) ] c
3
T
s 
1/ 2

g b Q T
dE  [ 1  exp[(
1
E b ) /T ]
2
6M
2
45
2
g T
3
  nB / s 
15 c
4
2
g b Q
g  MT
The value of depends on the model of Quintessence
Cosmological CPT violation!

1
1  exp[( E   b ) / T ]
]
Leptogenesis
Anomaly for CMB
Cosmological CPT violation: predicting <TB> and <EB>
 Q    f (R)
Hong Li et al
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
\delta\alpha=-2.33 \pm 0.72
\delta\alpha= -0.04 \pm 0.37 deg
With WMAP7+B03+BICEP
with WMAP7+B03+BICEP+QUaD
Interacting DE, Cosmological CPT violation and CMB test
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 !
Relevant papers
1） Probing CPT Violation with CMB Polarization Measurements.
Jun-Qing Xia, Hong Li, Xinmin Zhang, e-Print: arXiv:0908.1876
2）Testing CPT Symmetry with CMB Measurements: Update after WMAP5.
Jun-Qing Xia, Hong Li, Gong-Bo Zhao, Xinmin Zhang,
Astrophys.J.679:L61,2008
3）Testing CPT Symmetry with CMB Measurements.
Jun-Qing Xia, Hong Li,
Xiu-lian Wang, Xin-min Zhang, Astron.Astrophys.483:715-718,2008
4）Cosmological CPT violation, baryo/leptogenesis and CMB polarization.
Mingzhe Li, Jun-Qing Xia,, Hong Li, Xinmin Zhang, Phys.Lett.B651:357-362,2007
5）Searching for CPT Violation with Cosmic Microwave Background Data from WMAP
and BOOMERANG.
Bo Feng,, Mingzhe Li,, Jun-Qing Xia, Xuelei Chen,, Xinmin Zhang
Phys.Rev.Lett.96:221302,2006.
6） Testing the Lorentz and CPT Symmetry with CMB polarizations and a nonrelativistic Maxwell Theory.
Yi-Fu Cai, Mingzhe Li, Xinmin Zhang, JCAP 1001:017,2010.
7）$CPT$ Violating Electrodynamics and Chern-Simons Modified Gravity.
Mingzhe Li, Yi-Fu Cai, Xiulian Wang, Xinmin Zhang,
Phys.Lett.B680:118-124,2009
8）Cosmological CPT violating effect on CMB polarization.
Mingzhe Li, Xinmin Zhang, Phys.Rev.D78:103516,2008.
Sources of the CMB polarization
for the B-mode:
i)Tensor perturbation;
ii)CPT violating effect;
iii)Lensing
…….
Quintessino As Dark Matter
•If susying the Quintessence:
Quintessence: Q
Squintessence: σ
Quintessino:
(X. Bi, M. Li
and Zhang)
q
Similar to : Axion, Saxion, Axino
Majoron, Smajoron, Majorino (R. Mohapatra and Zhang)
•If is lighter than  ,
could serve as Dark matter
•Susying the following interaction
(H: SU(2) doublet)
gives
gives
* Prediction: long-lived charged particle:
Summary
1) Current status on constraints on dark energy:
a) Cosmological constant fits data well;
b) Dynamical model not ruled out;
2) Interacting DE with derivative couplings
==== cosmological CPT violation
=====Quintessential Baryo/Leptogenesis
3) Cosmological CPT violation tested with CMB
CMB photon travelling over the distance around
the observed universe,
provides the most sensitive test to CPT!
(anomalous Axion string effect ?)