Outline
• Importance of cosmological perturbations• Dark energy models• Dark energy perturbations• Dark energy coupling to CMB photons I• Dark energy coupling to CMB photons II• Conclusions
3/1
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Accelerating universe
Negative pressure
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pg
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1w
1, Cosmological Constant (Einstein 1917)
No perturbation
43 )102( eV
Cosmological constant problem
Observation
Zero point energy density
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mkk
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2, Dynamical dark energy
I, quintessence Peccei, Sola, Wetterich, 1987 Wetterich, 1988 Peebles, Ratra, 1988 Zlatev, Wang, Steinhardt, 1998
)()(2/1 2 VL
)()(2/1 2 VL
1 ,2/1 ,12/1
2/1 22
2
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Vw
II, phantom Caldwell, 1999
12/1
2/12
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Vw
2)1/2(X ),( XKL
III, k-essence Amendariz-Picon, Mukhanov, Steinhardt, 2000
XXppKp 2 ,
Quintessence, phantom are special cases of k-essence
W cannot cross -1
IV, quintom w crosses -1
),()(2/1)(2/1 212
12
1 VL Feng, Wang, Zhang, 2004
)()()(2/1 222
2 VM
cL ML, Feng, Zhang, 2005
22)(1)( VL Cai, ML, Lu, Piao, Qiu, Zhang, 2007
W a crucial parameter to distinguish different models
Data fitting, model independent, parameterization
DE perturbation, only vanished when w=-1 (cosmological constant)Naively switch off DE perturbation is not consistent
Using observational data to search for DE models
))(( 222 jiij dxdxdads
TGG 8
FRW background
Metric perturbation
Equations of perturbations
0 T
Conformal Newtonian Gauge
Dark Energy Perturbations
: sound speed in the comoving frame
Adiabatic sound speed
Single fluid
Quintessence, phantom
0
K-essence )2/(/2XXXXXXs Xppppc
Equations of dark energy perturbation
The problem of dark energy perturbations
Singular when w_e crosses -1No-Go Theorem J.Xia, Y.Cai, T.Qiu, G.Zhao, X.Zhang (2008) Quintom dark energy B.Feng, X.Wang, X.Zhang (2005)More degrees of freedom
Parameterization, e.g.,
Multi fluids or multi fields need more equations
not applicable
Not convenient in data analysis
Method without new parameters Zhao, Xia, ML, Feng, Zhang, 2005
Quintessence like
Phantom like
Matching conditionML, Cai, Li, Brandenberger, Zhang, 2010
Space-like surface :
The induced 3-metric on and its extrinsic curvature be continuous on both sides
go to the “tilde coordinate system”
Adiabatic perturbation
.constr
Isocurvature perturbationr
Mixture of adiabatic and isocurvature modes
The action integral is gauge invariant.
Geometric Optics Approximation
Dark energy coupling to photons I: Chern-Simons and CPTviolation
M
cp
Stokes parameters
I→ intensity Q&U→ linear polarization V→ circular polarization
ieUQiUQ 222
The polarization angle: Q
Uarctan
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Spin 2
CPT violation induced the rotation of the polarization direction
Rotation angle characterizes the CPT-violating effect!
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ml
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lmobs
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Without CPT violation, the correlations of TB and EB vanish
Consider the rotation angle as a free parameter
Perturbation, spatial dependent rotation angle
ML, Zhang, 2008
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A new method to produce B-mode polarization
CPT violation
Weak gravitational lensing W.Hu 2000
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Weak gravitational lensing
Conclusions
• Naively turn off dark energy perturbation is not consistent.
• We need new method to treat the dark energy perturbation in the whole parameter space.
• DE isocurvature perturbation is not strongly constrained by current data, but it is expected to be limited more tightly by CMB-LSS cross correlation.
• In models of dark energy interacting with photons, the perturbation of dark energy has interesting implications.
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