暗能量和宇宙学 CPT破坏

李明哲南京大学物理系

粒子 - 核 -宇宙学联合研究中心

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

SN Ia (SCP, HZT….)

LSS (2dfGRS, SDSS…)

Brief Review on Dark EnergyAccelerating Universe ->Dark Energy

CMB experiments

Dark matter?Dark energy?Why no antimatter?……

No antimatter

Candidates:1, Cosmological constant

/ 1w p

Cosmological constant problem! 412343 10~)10(~ plmeV

gT

0)3(3

4 p

G

a

a

3/1/ pw

Negative pressure

S. Weinberg, RMP (1989)

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

2 2 22

1( ) ( ) ( )

2

cL V

M

2''1)( VL Cai,Li,Lu,Piao,Qiu&Zhang, PLB(2007)

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).

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 GeVKuzmin, Rubakov&Shaposhnikov,PLB(1985)

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:

Mingzhe Li, Jun-Qing Xia, Hong Li, Xinmin Zhang, PLB (2007)

The Model

iJM

cL

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.

This CPT violation can be observed by CMB polarization experiments!

iJM

cL

The full lagrangian of photons

The action integral is gauge invariant.

Geometric Optics Approximation

Basic equations:

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

Local Lorentz frame

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

Observation of cosmological CPT violation through CMB experiments

In the case of homogeneous

Without CPT violation, the correlations of TB and EB vanish

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)

Spatial dependent rotation angle:Mingzhe Li & Xinmin Zhang, PRD(2008)

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, PRL(2009), 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.

Thanks!

Date: Wed, 8 Oct 2008 21:04:24 -0700From: Marc Kamionkowski <kamion@tapir.caltech.edu>To: Zhang XinMin <xmzhang@mail.ihep.ac.cn>Subject: polarization rotation

Hi Xinmin,

Enclosed below is a paper that you might be interested in. It follows on work that you finished just recently.

Cheers,

Marc

From: Meng Su <mengsu@cfa.harvard.edu> To: xmzhang@mail.ihep.ac.cn Date: 2009-02-27, 15:32:45Subject: Greetings from Meng Su

Dear Prof. Zhang

This is Su Meng if you still remember:) Now I'm studying at HarvardUniversity working with Prof. Matias Zaldarriaga. Haven't met you for awhile, how is everything going with you?Recently you had a work with Dr. Li Minzhe about spacial dependent rotationof CMB polarization. I thought it is very interesting! I wrote an email toDr. Li but didn't get reply... So Kamionkowski after then had a work aboutreconstruct the rotation field from CMB polarization. I suggested peoplehere to work on this topic and we just have a paper online arXiv: 0902.4466.First of all, I hope this paper cite your previous papers on this topicswell:)………………………….

Best regards,

Meng Su