cosmological cpt violation, baryo/leptogenesis and cmb polarization mingzhe li nanjing university
TRANSCRIPT
Outline1, Brief review on dark energy models, cosmological constant or dynamical
dark energy, current status
2, Interacting dark energy:
direct coupling:
propagates long range force, spoils the flatness of the potential of dark energy
derivative coupling:
spin-dependent force, shift symmetry, guarantee the flatness of the potential, cosmological CPT violation
3, Model: LLBJL )(~
Leptogenesis Anomaly for CMB
4, Conclusion
,...),,(
GFO
,...),,(
GGFFL
Brief Review on Dark Energy Models
Negative pressure
3/1/ pw
Candidates:1, Cosmological constant
/ 1w p
Cosmological constant problem! 412343 10~)10(~ plmeV
gT
2, Dynamical dark energy21
( ) ( )2
L V 2
2
1/ 2
1/ 2
Vw
V
Quintessence: 1 1w
0w
Phantom: 21( ) ( )
2L V 1w
eVHVmeff33
0 10~)(''
K-essence: ( , )L L 1, 1w w
Cannot cross -1, no-go theoremFeng, Wang & Zhang, PLB(2005);Vikman, PRD(2005);Zhao, Xia, Li, Feng & Zhang, PRD(2005); Xia, Cai, Qiu, Zhao &Zhang, IJMPD(2008)
Quintom:
2 21 2 1 2
1 1( ) ( ) ( , )
2 2L V Feng, Wang & Zhang, PLB(2005)
2 2 22
1( ) ( ) ( )
2
cL V
M Li, Feng & Zhang, JCAP(2005)
wcrosses -1
………
Flat potential
It is important to determine w of DE by cosmological observations!
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)
Current constraint on the equation of state of dark energy
WMAP5 resultE. Komatsu et al., arXiv:0803.0547
Xia, Li, Zhao, Zhang, PRD(2008)
Status: 1) Cosmological constant fits data well;2) Dynamical model not ruled out;3) Best fit value of equation of state: slightly w across -1 Quintom model
Quintessence
phantom
Quintom A
Quintom B
Dynamical dark energy is expected to have interactions to the rest of the world besides the gravity.
Two types of couplings: direct & derivative
1, direct coupling
Interacting Dark Energy
,...),,(
GGFFLM
c
eVm 3310
)(10 4
plM
Mc
A. Long range force
Constrained tightly! S.M. Carroll, PRL(1998)
B. Instability under quantum corrections
meV
Mm
7
2
10~4 ewplMM ~,~
2, derivative coupling:
cosmological CPT violation!
1, obeys the shift symmetry which guarantees the flatness of the potential.
2, propagates spin-dependent force, short range, much weaker constraint from astrophysics PDG(2002)Violates Lorentz and CPT symmetry because
.const
00
,...),,(
GFOM
c
00101 )()()()( OCPTOCPTCPTOCPT
GeVM 1010
1010~
n
n
n
nn
n
n bbbB sn ~
Cosmological CPT violation and baryogenesis
The universe is not symmetric between matter and antimatterWe need baryogenesis
• Baryon number non-conserving interaction
• C and CP violations
• Departure from thermal equilibrium
Sakharov conditions for baryogenesis:
Precondition: CPT is conserved!
Cohen & Kaplan, PLB(1987)
Interacting dark energy and baryogenesis
A unified picture of matter-antimatter asymmetry and dark energy!
Albrecht & Skordis, PRL(2000)
)exp()()( plM
fV
Quintessence model with tracking solution
Copeland, Liddle & Wands, PRD(1998).
1, The electroweak Sphaleron violates B+L and will makeas low as 100GeV, M should be GeV
DT1010
2, If M is higher, e.g., GUT scale or Planck mass scale, the generated baryon number asymmetry would be very small compared with the observation.
3, In this case, we turn to leptogenesis
Comments:
M
T
s
n DLB 210~
the decoupling temperature of B-L violating interaction. DT
Sphaleron conserves B-L and converts B-L asymmetry generated above to a same order of baryon number asymmetry.
GeVTMM Dplanck1010~,
Baryon isocurvature perturbation
Adiabatic or isothermal:
Isocurvature or entropy:
n
n
s
s
n
nsn
X
XX ,0)/(
0)/( snX
s
nBIn our case
The fluctuation of the dark energy scalar field will induce a nonzero baryon isocurvature perturbation
)exp()()( plM
fV The quintessence model with potential
)]()([ 212/1 kJCkJC
510)( planck
inreisocurvatu
B
B
M
H
n
n
Consistent with the observations!
M
GeV
MV
2230
0
10~
In our model of baryo/leptogenesis
The CPT violation is very small, was large to generate enough baryon number asymmetry in the early universe.
The full lagrangian of photons
The action integral is gauge invariant.
Geometric Optics Approximation
Polarization and Stokes parameters
At the inertial frame
I→ intensity Q&U→ linear polarization V→ circular polarization
ieUQiUQ 222
The polarization angle: Q
Uarctan
2
1
CPT violation induced the rotation of the polarization direction
Rotation angle only depends on the difference of dark energy field at the source and the observer’s positions.
Which characterize such CPT-violating effect!
)( f
i
f
iif dxpdkp
M
cp em
3
2
WMAP3 only
: 0.057 degPLANCK
deg 0.40.6
deg 8.32.6
1)
2)
3)
6)
Bo Feng et al., PRL 96, 221302 (2006)
J.Q.Xia et al., arXiv:0710.3325
5) J.Q.Xia et al., arXiv:0803.2350
4) (WMAP Group) Komatsu et al., arXiv:0803.0547
WMAP5 only
J.Q.Xia et al., arXiv:0710.3325
deg 0.35.2
deg 1.27.1 deg 9.16.2
P.Cabella, Natoli & Silk, PRD (2007)
This is the direct consequence of invariance of under the rotation
sin, ,, obsEBl
obsTBl CC
Only the background evolution of dark energy provides CPT violation!
The corrections are at the order of 2
In the quintessence model with tracking potential,
)]()([ 212/1 kJCkJC
222
2 )10
(~M
eV
By assuming the initial fluctuation of quintessence generated from a GUT scale inflation
Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization.Yadav, Biswas, Su, Zaldarriaga,arXiv:0902.4466
How to De-Rotate the Cosmic Microwave Background Polarization.M. Kamionkowski, arXiv:0810.1286
Detection of Spatially Dependent Rotation Angle
Conclusion
• Dynamical dark energy has possible couplings besides gravity to other matter. Direct couplings are constrained tightly. Derivative couplings are more likely.
• The derivative couplings violate CPT cosmologically and can explain the matter-antimatter asymmetry.
• Our model of leptogenesis predicts CPT violation in the photon sector. It can be tested by CMB, current data favored nonzero rotation angle mildly.
• The rotation angle is anisotropic in general. More studies in the future.