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.

ccosmo

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!