CMB power spectra from the coupling between

quintessence and pseudoscalar of electromagnetism

Guo Chin Liu (ASIAA)Seokcheon Lee(ASIoP)

Kin-Wan Ng (ASIoP, ASIAA)

The 2nd KIAS WORKSHOP ON COSMOLOGY AND STRUCTURE FORMATION

Necessary of Dark energy

Hubble Diagram for SCP

1.Cosmological constantCost of having space: a volume of space have intrinsic energyconstant on space and timeProblem: 120 orders of magnitude smaller than prediction by quantum field theories

2.QuintessenceDescribed by dynamical scalar field Can vary with space and time

Cosmological constant and Quintessence

V()=V0e(52/2) V()=V0cosh(5)

Equation of state w=p/

1. Supernova type Ia : probe the geometry of universeCaution: assuming uniform intrinsic luminosity

2. CMB : good constraint on small curvatureCaution : no time evolution data

3. Large scale structure : evolution of geometry of universe and growth factor D(z) Caution: depend on CDM model for structure formation

Cosmological constant: w=-1

Quintessence : wQ: w0, w0+(1-a)w1, oscillating….

a. Assume flat universe and const. ww=-1.05+0.15-0.2

Knop et al.2004 (SN)b. time evolution w=w0+ (1-a)w1

w0=-1.146+0.176-0.178 w1=0.6+0.622-0.652 --no dark energy perturbationw0=-1.118+0.152-0.147w1=0.499+0.453-0.498 -- with dark energy perturbation

G-B Zhao et al. 2006(SN+CMB+galaxy clustering)

Quintessence survivesNo strong evidence that we need it

New window on studying Quintessence1.Coupling with matter

-- change the CMB and matter power spectrum

S. Lee, GC Liu & KW Ng 2006

2.Coupling with electromagnetic field-- time variation of fine structure

D-S Lee, W Lee, K-W Ng 2003, S.Lee, K. Olive, M. Pospelov

3.Coupling with psuedoscalar eletromagnetismFF/M => cosmological birefringence effect

Carroll 1998

: coupling strength

M: reduced Planck Mass

F : dual of electromagnetic tensor

Cosmological Birefringence -- rotate the pol. plane

Dispersion : E2=k2kd/d/a/M=2 d/d/a/M

1.Generate B mode polarizationassuming no tensor perturbationGenerate Stokes parameter U due to rotationB mode because of the existence of U in local coordinate

2.Violate the parityLue et al. 1999, Lepora 1998

Effects from Cosmological Birefringence

<TT>, <TE>, <EE>, <BB>

+ <EB>, <TB> parity violation part

E and B mode power spectrum

C’Bl=CEl*sin2(2)C’El=CEl*cos2(2)

EB power spectraCEBl=0.5CEl*sin(4)

TE and TE power spectrum

CTBl=CTEl*sin(2)

C’TEl=CTEl*cos(2)

Constraint from current CMB data

WMAP 3-year data

Even no clear detection, we can give the upper limitUsing Boomerane 2003 data

TB, EB and BB from Birefringence and Boomerang

Likelihood function2 fitting L=e -0.52

use TB and EB only/M < 8.32*10-4 95% CL

/M < 3*10-2 95%CLCarroll 1998

Summary

1. CMB offers another opportunity to study quintessence

through parity violation

2. Better constraint than quasar’s pol. rotation data

3. Similar to effect from Faraday rotation, but no freq.

dependence here