May 10, 2011 IHEP Beijing

CPT theorem: any local and Lorentz covariant quantum field theory with hermitian Hamiltonian must have CPT symmetry.
Cosmological CPT violation
 
0
    
0
L int
 c



O

(

, F

, G

,...)
 c
M
 
O
0
M
(

CPT
  
( t
) c
1 c
) o s
O
 
( t
0
(
) O

 x
0
(
,
 t
 x
)
, t

)( CPT
 
(
 t
)
) O

0
(
 

( t
 x ,
)( CPT
 t )
)

1
O
0
(
 x , t )( CPT )
(
m o
)

1
int
(
)

int

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)

Quintessence model with tracking solution
V (

)
 f (

) exp(

M
 pl

)
Albrecht & Skordis, PRL(2000)
Copeland, Liddle & Wands, PRD(1998).

g



 g
 s

100 , g b

2

10

2
,

2 
100
Bean, Hansen & Melchiorri, PRD(2001);
Doran & Robbers, JCAP(2006)

Comments:
1, The electroweak Sphaleron violates B+L and will make T
D
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

ML, J. Xia, H. Li & X. Zhang, PLB (2007)
L
 c
M



J i


n
B

L s
~ 10

2
T
D
M
T
D the decoupling temperature of B-L violating interaction.
Sphaleron conserves B-L and converts B-L asymmetry generated above to a same order of baryon number asymmetry.
M

M planck
, T
D
~ 10
10
GeV

Electromagnetic anomaly
L
 c
M



J i

Generate cosmic birefringence, may be detected by astrophysics and CMB

Cosmological CPT violation and cosmic birefringence
The action integral is gauge invariant.
In flat space
F

F

''

( k
2

B y
 2 p
0 k ) F

 iB z

0 k
 tan

( k , k , 0 , 0 )
 
B
B z y
  i
F
F




F

F


In curved spacetime
Geometric Optics Approximation
Basic equations:

I → intensity Q&U→ linear polarization V→ circular polarization
Q
 iU
The polarization angle:

 
1
Q
2 arctan
2

U
2
U
Q e

2 i

Spin 2

In curved spacetime, introduce tetrads

Cosmic birefringence: rotation of the polarizaton direction
I obs 
I
Rotation angle
    f
  i
   i f p
 k
 d
    i f p
 dx

(

) p

 const .
p

 c
M



 
  
 p

( x i
  c
(
 i
M
  f x
 f
)
)

Spherical multi-pole expansion
T ( n
ˆ
)
( Q

 iU
 lm a
T , lm
Y lm
( n
ˆ
)
)( n
ˆ
)
   lm
( a
E , lm
 ia
B , lm
)

2
Y lm
( n
ˆ
) a
T , lm a
E , lm
  d

Y
* lm
( n
ˆ
) T ( n
ˆ
)
 ia
B , lm
   d


*
2
Y lm
( n
ˆ
)( Q
 iU )( n
ˆ
)
Power spectra
 a
*
X ,' l ' m ' a
X , lm

C l
XX '
 ll '
 mm '
X , X '

T , E , B
C l
TT
, C l
EE
, C l
BB
, C l
TE
, C l
TB
, C l
EB

Scalar r=0.22
Tensor
TB, EB vanish in standard LCDM model
Challinor & Peiris (2009)

E-mode polarization, first detected by DASI 2002

Power spectra changed by cosmic birefringence
( a
E , lm
 l
1
 m
1
 ia
B , lm
) obs
( a
E , l
1 m
1
   d



2
Y lm
( )( Q
 iU ) obs
(
ˆ
)
 ia
B , l
1 m
1
)
 d



2
Y lm
(
ˆ
) exp(
 i 2
 
)

2
Y l
1 m
1
(
ˆ
)
For homogeneous rotation angle
( a
E , lm
 ia
B , lm
) obs  exp(
 i 2
 
)( a
E , lm
 ia
B , lm
)

Without CPT violation, the correlations of TB and EB vanish
Consider the rotation angle as a free parameter

Simulation result :
CMBPol can detect
  
0 .
0001


WMAP3+BOOMERanG03
   
6 .
0

4 .
0 deg

1) WMAP Group
   
1 .
1

1 .
3 deg
Komatsu et al., arXiv:1001.4538
2) WMAP Group
   
1 .
7

2 .
1 deg
Komatsu et al., arXiv:0803.0547, ApJS(2009)
3) QUaD Group
  
0 .
64

0 .
5 deg
M.L. Brown et al., arXiv:0906.1003, ApJ(2009)
4)
   
2 .
5

3 .
0 deg
P.Cabella, Natoli & Silk, PRD (2007)
5)
   
6 .
2

3 .
8 deg
J.Q.Xia et al., A&A (2008)
6)
7)
   
2 .
6

1 .
9 deg
PLANCK :
 
0.057 deg
J.Q.Xia et al., ApJL(2008)
J.Q.Xia et al., A&A (2008)

WMAP5+B03+BICEP
   
2 .
6 2

0.87deg(68 %C.L.)
WMAP7+B03+BICEP
WMAP7+B03+BICEP+QUaD
 
 
 
2 .
33

0.72deg(68 %C.L.)
 
0.04

0.35deg(68 %C.L.)
Jun-Qing Xia, Hong Li & Xinmin Zhang, PLB (2010)

CMB polarization:
Comparison with laboratory CPT test p


( p
0 ,
0 , 0 , 0 ), p
0
 const.
   p
0
(
 dec
 
0
) ~
 p
0
|
 p
0

~
|~ 1
 

0 .
1 H
0
180
~ 10

43
GeV
H
0
Laboratory: spin-polarized torsion pendulum experiments
L
 p

   
5
  p
0
 
0

5

Consider the velocity of the earth relative to the CMB rest frame
L
 p
0


 v
 earth
To electrons
| p
0
|

1 .
2

10

28
GeV
Heckel et al. (2008)

Explicit:
T
F
  


.
2 g

S
F
 g


1
4
F
2 g
 
F

F


Gravitational field equation
G
 
R
 
1
2
Rg



T
F
 
1
2 p

F
~
F

0
 
8

G ( T
M
 
T
F

)
Einstein tensor symmetric and


G
 
0 Inconsistent!

L g

1
16

G
R

1
16

G
( R


4
R
~
R )
~
R R

1
2
 
R


R


,
  q
 x

G
 
C
  
8

G ( T
M
 
T
F

)


C

Constraint

1
 q
8
~
R R q

~
R R
 
32

Gp

~
F F
ML, Y. Cai, X. Wang & X. Zhang, PLB(2009)

CPT violation in gravity causes different spectra for left and right handed tensor perturbations and generates TB and EB of CMB at LSS.
TB and EB on RHS are due to R
~
R

Spontaneous: p

 c
M





( T
F
 
T


)

0
Not necessary to modify the gravity!
   c
M
(
 i
  f
)
 c
M
 
Rotation angle depends on time as well as space

Spatial dependent rotation angle:
ML & X. Zhang, PRD(2008)
C l
 
4
 c
2
M
2
 dk
P
 k
( k ,
 dec
) j l
2
[ k (

0
  dec
)]

A new method to produce B-mode polarization
CPT violation
C l
BB , obs 
[ C l
EE sin
2
( 2
 
)

C l
BB cos
2
( 2
 
)]( 1

4
  
2 
)

 l
1 l
2

 l l
1 l
2
2

2 0


2
( 2 l
1

1 )(
2

2 l
2

1 )
C l

2
[ C l
1
EE

C l
1
BB

(

1 )
L cos( 4
 
)( C l
1
EE

C l
1
BB
)]
Weak gravitational lensing W.Hu 2000
~
C l
BB 
[ 1
 l
2  l
8


4  l
1 l
1
( l
1

1 )( 2 l
1

1 ) C
 l
1
] C l
BB 
 l
1 l
2
[ l
1
( l
1
C l

2
[ C l
1
EE

1 )
 l
2
( l
2

C l
1
BB

1 )
 l ( l

(

1 )
L
( C l
1
EE

1 )]
2

 l l
1 l
2
2

2 0

C l
1
BB
)]


2
( 2 l
1

1 )( 2 l
2
16


1 )

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
 

( n

• 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 Bmode polarization at late time.