Testing CPT with CMB

李明哲University of Bielefeld

2008 年 4 月 28 日

"for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation".

John C. Mather & George F. Smoot

CMB (Maxima, Boomerang, WMAP)SN Ia (SCP, HZT,SNLS,ESSENCE)LSS (2dfGRS, SDSS)

Precision Cosmology

Concordance ModelInflation + Dark Matter + Dark Energy

Problems:1, What is inflaton? What happened in detail during inflation?2, What is dark matter particle?3, What is dark energy?4, Why no anti-matter?

Outline

• Brief review on dark energy models

• Interacting dark energy, cosmological CPT violation and baryogenesis

• Testing CPT with CMB

• Summary

Brief review on dark energy modelsEinstein equation: 4

( 3 )3

a Gp

a

π ρ=− +&&

0a >&& 1

3

pw

ρ≡ <−

Negative pressure and almost not cluster

Candidates:1, Cosmological constant (or vacuum energy)

1w =− 3 4 123 4 44 4 60 4(2 10 ) 10 10 10pl QCD SUSYeV mρ − − − −≈ × Λ Λ: : :

Cosmological constant problem! S. Weinberg, RMP(1989)2, Dynamical fields Quintessence

22

2

1 1/ 2( ) ( ), 1 1

2 1/ 2

VL V w

V

φφ φφ

−= ∂ − − ≤ = ≤

+

&&

2 Vφ& = 1w ≈−

22

2

1 1/ 2( ) ( ), 1

2 1/ 2

VL V w

V

φφ φφ

− −=− ∂ − = <−

− +

&&Phantom

2 21 2 1 2

1 1( ) ( ) ( , )

2 2L Vφ φ φ φ=− ∂ + ∂ −

Quintom w crosses -1

2 2 22

1 1( ) ( ) ( )

2L V

Mφ φ φ= ∂ + ∂ −

Feng, Wang & Zhang, PLB(2005)

Li, Feng & Zhang, JCAP(2005)

Phantom

Quintessence

Quintom A

Quintom B

Current constraints on dark energy models

No-Go TheoremFor theory of dark energy (DE) in the 4D Friedmann-Robertson-Walker (FRW) universe described by a single perfect fluid or a single scalar field with a largangian of , which minimally couples to Einstein Gravity, its equation of state w cannot cross over the cosmological constant boundary.

A challenge to dark energy theories

( , )L L μμφ φ φ= ∂ ∂

1 0, 0 , , ,w w δ θ δ θ+ → ≠ ⇒ → ∞&&&Quintom models with double fields or higher derivatives can avoid this problemZhao, Xiao, Li, Feng & Zhang, PRD(2005).

Interacting dark energy, cosmological CPT violation and baryogenesis

Matter-antimatter asymmetry (Baryon number asymmetry)

BBN, CMB, …

Since Dirac, fundamental theories are not biased between matter and antimatterWe need baryogenesis: the process to produce baryon number asymmetry

€

nB

nγ

≡nb − n

b

nγ

~ 10−10

€

nb

nγ

= 0

• Baryon number non-conserving interaction• C and CP violations• Departure from thermal equilibrium

Sakharov conditions for baryogenesis:

Precondition: CPT is conserved!

CPT Theorem

If a field theory: 1) is local; 2) is Hermitian; 3) is Lorentz covariant; 4) satisfies spin-statistic relations;CPT is conserved

€

<∇μφ >=(∇ 0φ,0,0,0) ≠ 0

The rolling of dark energy scalar field breaks Lorentz covariance

It provides a source to violate CPT, e.g.,

€

L ~ ∇ μφJ μ

Cosmological CPT violation

Generalization

CPT violation in photon sector; P and CP are also violated

Testing CPT with CMB

The CPT violating term is potentially observable with photons polarization

Polarization and Stokes parameters

General definition of Stokes parameters

M.Li et al, work in progress

CMB polarization

P.Cabella, Natoli & Silk, PRD76, 123014 (2007)

Bo Feng et al., PRL 96, 221302 (2006)

J.Q.Xia et al., arXiv:0710.3325

J.Q.Xia et al., arXiv:0803.2350

(WMAP Group) Komatsu et al., arXiv:0803.0547

J.Q.Xia et al., arXiv:0710.3325

6.0 4.0 degαΔ =− ±

WMAP3 only2)

1)

6.2 3.8 degαΔ =− ±3)

4) WMAP5 only1.7 2.1 degαΔ =− ±2.6 1.9 degαΔ =− ±

: 0.057 degPLANCK σ =

5)

6)

Summary

• Precision cosmology supports the model of the universe with dark energy and current data favors slightly quintom dynamical dark energy.

• Interacting dark energy induces cosmological CPT violation, can be tested by CMB and current data provides a weak evidence for such a CPT v

iolation.