S. Weinberg, RMP (1989)
2, Dynamical dark energyw 0
Quintessence: L 1 ()2 V ()
2
w
1/ 1/
2 2
2 2
V V
1 w 1
meff V ' ' () H0 ~ 1033 eV Flat potential
Phantom: L 1 ()2 V () w 1
2, propagates spin-dependent force, short range, much weaker constraint from astrophysics
M 1010GeV PDG(2002)
Violates Lorentz and CPT symmetry because
1, direct coupling
c
M
L( , F F
, G G
,...)
m 1033eV
A. Long range force
c 10 4 ( M ) Constrained tightly! S.M. Carroll, PRL(1998) M pl
B. Instability under quantum corrections
direct coupling: L( , F F ,G G ,...)
propagates long range force, spoils the flatness of the potential of dark
energy
derivative coupling: O ( , F ,G ,...)
Sakharov conditions for baryogenesis: • Baryon number non-conserving interaction • C and CP violations • Departure from thermal equilibrium
Precondition: CPT is conserved!
L
c M
J
i
This CPT violation can be observed by CMB polarization experiments!
The full lagrangian of photons
The action integral is gauge invariant.
Geometric Optics Approximation
Status: 1) Cosmological constant fits data well; 2) Dynamical model not ruled out; 3) Best fit value of equation of state:
slightly w across -1 Quintom model
Comments:
1, The electroweak Sphaleron violates B+L and will make TD
as low as 100GeV, M should be 1010GeV Kuzmin, Rubakov&Shaposhnikov,PLB(1985)
2, If M is higher, e.g., GUT scale or Planck mass scale, the generated baryon number asymmetry would be very small compared with the observation.
Adiabatic or isothermal:
(nX
/
s)
0, nX
nX
s n
s n
Isocurvature or entropy: (nX / s) 0
In our case nB
s
The fluctuation of the dark energy scalar field will induce a nonzero baryon isocurvature perturbation
V () f () exp( )
M pl
Albrecht & Skordis, PRL(2000)
Copeland, Liddle & Wands, PRD(1998).
g gs 100 , gb 2
102 , 2 100
Bean, Hansen & Melchiorri, PRD(2001); Doran & Robbers, JCAP(2006)
Sphaleron conserves B-L and converts B-L asymmetry generated above to a same order of baryon number asymmetry.
M M planck ,TD ~ 1010GeV
Baryon isocurvature perturbation
a 4G ( 3 p) 0
a3
w p / 1/ 3
Negative pressure
Candidates:
1, Cosmological constant
T g w p / 1
Cosmological constant problem!
~ (103eV )4 ~ 10123m4pl
3, In this case, we turn to leptogenesis
The Model
Mingzhe Li, Jun-Qing Xia, Hong Li, Xinmin Zhang, PLB (2007)
L
c M
J
i
nBL ~ 102 TD
s
M
TD the decoupling temperature of B-L violating interaction.
………
It is important to determine w of DE by cosmological observations!
Parameterization of equation of state: A) w=w_0+w_1 z (for small z) B) w=w_0+w_1 z / (1+z) (used mostly in the literature) C) w=w_0+w_1 sin(w_2 ln(a)+w_3)
Current constraint on the equation of state of dark energy
Quintom A
Quintessence
phantom
Quintom B
WMAP5 result E. Komatsu et al., arXiv:0803.0547
Xia, Li, Zhao, Zhang, PRD(2008)
暗能量和宇宙学CPT破坏
李明哲 南京大学物理系 粒子-核-宇宙学联合研究中心
Outline
1, Brief review on dark energy models, cosmological constant or dynamical dark energy, current status
2, Interacting dark energy:
Cohen & Kaplan, PLB(1987)
Interacting dark energy and baryogenesis A unified picture of matter-antimatter asymmetry and dark energy!
Quintessence model with tracking solution
2
K-essence: L L(,) w 1, w 1
Cannot cross -1, no-go theorem
Feng, Wang & Zhang, PLB(2005);Vikman, PRD(2005);Zhao, Xia, Li, Feng & Zhang, PRD(2005); Xia, Cai, Qiu, Zhao &Zhang, IJMPD(2008)
Basic equations:
Polarization and Stokes parameters
At the inertial frame
I→ intensity Q&U→ linear polarization V→ circular polarization
Q iU Q2 U 2 e2i
The quintessence model with potential V () f () exp( )
M pl
1/ 2[C1J (k) C2 J (k )]
(
nB nB
)isocurvature
H in M planck
10 5
Consistent with the observations!
Quintom:
w crosses -1
L
1 2
(1)2
1 2
(2
)2
V
(1,2 )
L
1 2
( )2
c M
2
( 2 )2
V
( )
Feng, Wang & Zhang, PLB(2005) Li, Feng & Zhang, JCAP(2005)
L V () 1 ' '2 Cai,Li,Lu,Piao,Qiu&Zhang, PLB(2007)
Interacting Dark Energy