Testing CPT with CMB
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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.
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