Download - Test CPT with CMB Mingzhe Li Department of Physics, Nanjing University May 10, 2011 IHEP Beijing
Test CPT with CMB
Mingzhe LiDepartment of Physics, Nanjing University
May 10, 2011 IHEP Beijing
Outline
• Cosmological CPT violation
• Test CPT with CMB polarization experiments
• Explicit and spontaneous CPT violations
• Conclusions
CPT theorem: any local and Lorentz covariant quantum field theory with hermitian Hamiltonian must have CPT symmetry.
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Cosmological CPT violation
Cosmological CPT Violation
0int ,...),,( O
M
cGFO
M
cL
00
),()(),()(
))(,())(())(,()()(00
0101
txOttxOt
CPTtxOCPTtCPTtxOtCPT
intint1 )()( SCPTSCPT
Cosmological CPT violation & baryogenesis
: dark energy
curvature
ML, X. Wang, B. Feng & X. Zhang, PRD(2002), ML & X. Zhang, PLB(2003),
Davoudiasl et al, PRL(2004) H. Li, ML & X. Zhang, PRD(2004)
Albrecht & Skordis, PRL(2000)
)exp()()( plM
fV
Quintessence model with tracking solution
Copeland, Liddle & Wands, PRD(1998).
2,100 bs ggg
100,10 22
Bean, Hansen & Melchiorri, PRD(2001);Doran & Robbers, JCAP(2006)
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. In this case we need leptogenesis
Comments:
iJM
cL
ML, J. Xia, H. Li & X. Zhang, PLB (2007)
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~,
iJM
cL
Electromagnetic anomaly
Generate cosmic birefringence, may be detected by astrophysics and CMB
The action integral is gauge invariant.
Cosmological CPT violation and cosmic birefringence
In flat space
FF
FFi
B
B
kkk
iBBF
FkpkF
y
z
zy
tan
)0,0,,(
0)2('' 02
Geometric Optics Approximation
In curved spacetime
Basic equations:
Stokes parameters
I→ intensity Q&U→ linear polarization V→ circular polarization
ieUQiUQ 222
The polarization angle: Q
Uarctan
2
1
Spin 2
In curved spacetime, introduce tetrads
Cosmic birefringence: rotation of the polarizaton direction
)( f
i
f
iif dxpdkp
M
cp )( fiM
c
II obs
.constp )( fi xxp
Rotation angle
Test CPT with CMB Polarization Experiments
)ˆ)()(ˆ(
)ˆ()ˆ(
)ˆ( )()ˆ)((
)ˆ()ˆ(
*2,,
*,
2,,
,
niUQnYdiaa
nTnYda
nYiaaniUQ
nYanT
lmlmBlmE
lmlmT
lmlmlmBlmE
lmlmlmT
Spherical multi-pole expansion
Power spectra
EBl
TBl
TEl
BBl
EEl
TTl CCCCCC ,,,,,
BETXX ,,', ''
',
*'',' mmll
XXllmXmlX Caa
Scalar Tensorr=0.22
Challinor & Peiris (2009)TB, EB vanish in standard LCDM model
E-mode polarization, first detected by DASI 2002
)ˆ()2exp()ˆ()(
)ˆ())(ˆ()(
11
11
1111 22,,
2,,
nYinYdiaa
niUQnYdiaa
mllmml
mlBmlE
obslm
obslmBlmE
For homogeneous rotation angle
))(2exp()( ,,,, lmBlmEobs
lmBlmE iaaiiaa
Power spectra changed by cosmic birefringence
Without CPT violation, the correlations of TB and EB vanish
Consider the rotation angle as a free parameter
0001.0CMBPol can detect
Simulation result:
Current Status
deg0.40.6 WMAP3+BOOMERanG03
: 0.057 degPLANCK
deg 8.32.6
4)
5)
7)
J.Q.Xia et al., A&A (2008)
6) J.Q.Xia et al., ApJL(2008)
Komatsu et al., arXiv:0803.0547, ApJS(2009)
J.Q.Xia et al., A&A (2008)
deg 0.35.2
deg 1.27.1
deg 9.16.2
P.Cabella, Natoli & Silk, PRD (2007)
1) WMAP Group
3) QUaD Group
deg 5.064.0 M.L. Brown et al., arXiv:0906.1003, ApJ(2009)
deg 3.11.1 Komatsu et al., arXiv:1001.4538
2) WMAP Group
%C.L.)0.72deg(6833.2 WMAP7+B03+BICEP
%C.L.)0.35deg(680.04WMAP7+B03+BICEP+QUaD
Jun-Qing Xia, Hong Li & Xinmin Zhang, PLB (2010)
WMAP5+B03+BICEP
%C.L.)0.87deg(6826.2
Comparison with laboratory CPT test
Laboratory: spin-polarized torsion pendulum experiments
To electrons GeV 102.1|| 280
p
5
005 ppL
Consider the velocity of the earth relative to the CMB rest frame
earth0 vpL
Heckel et al. (2008)
const. ),0,0,0( 0,0 ppp
0
000 ~)(
H
pp dec
GeV10~1.0~
1801|~|
4300
Hp
CMB polarization:
Explicit and spontaneous CPT violations
.constp Explicit:
FFgFg
S
gT FF 2
4
12
0~
2
1 FFpTF
Gravitational field equation
)(82
1 FM TTGRgRG
0 GEinstein tensor symmetric and Inconsistent!
)~
4(
16
1
16
1RRR
GR
GLg
xqRRRR ,2
1~
)(8 FM TTGCG
RRqC~
8
1
FFGpRRq~
32~ Constraint
ML, Y. Cai, X. Wang & X. Zhang, PLB(2009)
TB and EB on RHS are due to RR~
CPT violation in gravity causes different spectra for left and right handed tensorperturbations and generates TB and EB of CMB at LSS.
Spontaneous: M
cp
0)(
TTF
Not necessary to modify the gravity!
M
c
M
cfi )(
Rotation angle depends on time as well as space
Spatial dependent rotation angle:
ML & X. Zhang, PRD(2008)
)]([),(4
02
2
2
decldecl kjkPk
dk
M
cC
)])(4cos()1([2
)12)(12(
0 2 2
)41)](2(cos)2(sin[
11112
21
21
2
21
222,
BBl
EEl
LBBl
EEll
ll
BBl
EEl
obsBBl
CCCCClllll
CCC
)]()1([
16
)12)(12(
0 2 2
)]1()1()1([
])12)(1(8
41[
~
11112
21
1
1
21
2
2122211
111
2
BBl
EEl
LBBl
EEll
ll
BBll
l
BBl
CCCCC
lllllllllll
CClllll
C
A new method to produce B-mode polarization
CPT violation
Weak gravitational lensing W.Hu 2000
Recent progresses
(1) How to De-Rotate the Cosmic Microwave Background Polarization.Marc Kamionkowski, Phys.Rev.Lett.102:111302,2009. arXiv:0810.1286
(2) Constraining a spatially dependent rotation of the Cosmic Microwave Background Polarization.
Amit P.S. Yadav et al, Phys.Rev.D79:123009,2009. arXiv:0902.4466 (3) De-Rotation of the Cosmic Microwave Background Polarization: Full-Sky Formalism.
Vera Gluscevic, Marc Kamionkowski, Asantha Cooray,Phys.Rev.D80:023510,2009. arXiv:0905.1687 (4) Non-Uniform Cosmological Birefringence and Active Galactic Nuclei.
Marc Kamionkowski, Phys.Rev.D82:047302,2010. arXiv:1004.3544(5) Cross-Correlation of Cosmological Birefringence with CMB Temperature.
Robert R. Caldwell, Vera Gluscevic, Marc Kamionkowski,arXiv:1104.1634
Reconstruct the rotation angle )(n
Conclusions
• CPT violation in the early universe can be large enough to produce the observed matter-antimatter asymmetry and cosmic birefringence.
• Current CMB polarization experiments can be used to test CPT with high precision.
• CPT violation provides a new approach to produce B-mode polarization at late time.
Thanks!