Dark Energy Perturbations 李明哲 南京大学物理学院 中国科技大学交叉学科理论研究中心 合肥

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

Importance of cosmological perturbations

Inflation quantum fluctuation Primordial perturbation

1965 COBE WMAP CMB anisotropy

Tests of perturbation theory CMB Angular Power Spectrum

Matter Power Spectrum

Dark Energy (DE)

Accelerating universe Negative pressure 1, Cosmological Constant (Einstein 1917) No perturbation

Cosmological constant problem Observation Zero point energy density

2, Dynamical dark energy I, quintessence Peccei, Sola, Wetterich, 1987 Wetterich, 1988 Peebles, Ratra, 1988 Zlatev, Wang, Steinhardt, 1998 II, phantom Caldwell, 1999

III, k-essence Amendariz-Picon, Mukhanov, Steinhardt, 2000 Quintessence, phantom are special cases of k-essence W cannot cross -1 IV, quintom w crosses -1 Feng, Wang, Zhang, 2004 ML, Feng, Zhang, 2005 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

Without DE perturbation With DE perturbation Weller, Lewies, 2003 Constant w and sound speed

FRW background Metric perturbation Equations of perturbations Conformal Newtonian Gauge Dark Energy Perturbations

All matter including DE contribute to the metric perturbation

: sound speed in the comoving frame Adiabatic sound speed Single fluid Quintessence, phantom K-essence

Equations of dark energy perturbation The problem of dark energy perturbations Singular when w_e crosses -1 No-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

Fitting result with and without DE perturbation

Matching condition ML, 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”

Gauge transformation

Matching condition 3-metric extrinsic curvature

In arbitrary gauge In conformal Newtonian gauge

Gauge-invariant variables Initial conditions: adiabatic & isocurvature

Super-horizon scales

Adiabatic perturbation Isocurvature perturbation Mixture of adiabatic and isocurvature modes

Adiabatic perturbation

Pure dark matter isocurvature perturbation Ruled out by experiments

DE isocurvature perturbation Liu, ML, Zhang, 2010

The action integral is gauge invariant. Geometric Optics Approximation Dark energy coupling to photons I: Chern-Simons and CPT violation

Stokes parameters I→ intensity Q&U→ linear polarization V→ circular polarization The polarization angle: Spin 2

Six spectra

CPT violation induced the rotation of the polarization direction Rotation angle characterizes the CPT-violating effect!

Background homogeneous

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

CMBPol can detect Simulation result : Current Status

WMAP3+BOOMERanG03

Perturbation, spatial dependent rotation angle ML, Zhang, 2008

A new method to produce B-mode polarization CPT violation Weak gravitational lensingW.Hu 2000

Dark energy coupling to photons II: varying fine structure constant

Wang, ML, 2009 r: recombination

Linear fluctuation, new long range force

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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