The CP-violating inert-doublet model - Scalars 2011

Simple estimate
MPl
Density of dark matter given by Early Universe 3 〈σv〉
consideration:
Ω
Equilibrium between Hubble expansion and annihilation
DM h 2 = C T 0
3
WMAP:
Calculable
Ω DM h 2 = C T 3 0
M 3 Pl
Ω DM h 2 = C T 0
3 1
〈σv〉 = α2
MPl
3 〈σv〉 m 2
1
Ω
〈σv〉 DM h 2 =0.106 ± T0.008
0
and
ρ − 1=∆ρ ≃ αT = ¯T 〈σv〉 ⎧ = α2
F ( m 2 m
A,m ) ⎨ m2 2 A + 2
m2B
−
m2 AT m2 B
≡ B
T , R
⎩ 2 m 2 A − ln m2 0 m ∼ 100 A
m2 B
m 2 ⇐GeVm 2 A ≠ m2 B ,
B
0 ⎧ ⇐ m
m W = m 2 A = m2 B .
Z
F ( ) ⎨ m 2
G(m m 2
m W = m ⎧
A,m 2 A + m2 B
−
m2 A m2 B
B
B,m ≡ 2 Z) 2 m
Z
F ( ) ⎨ m 2
m
⎧ 2 A,m 2 A + ⎩ 2 A − ln m2 A
m2 B
m 2 ⇐ m 2 A
B
m2 B
−
m2 A m2 0
B
F ( ) ⎨ m 2 B ≡ 2 m
m 2 A,m 2 A + ⎩ 2 A − ln m2 A
m2 B
m 2 ⇐ m 2 A ≠ m2 B ,
⇐ m 2 A
H(m mass 2 A,mscale 2 B,m 2 Z) fits B
G(m well m2 B
−
m2 A m2 0 2 A,mwith B
B ≡ 2 m
⎩ 2 A − ln m2 A
m2 B
m 2 ⇐ m 2 A ≠ m2 B , ⇐ m 2 B,m 2
A = 2 Z) SUSY
m2 B .
B
0 t = I + JG(m − Q, 2 A,mr 2 B,m = ⇐Q Z) 2 −m 2 2Q(I
A = m2 + H(m
B . J)+(I 2 A,m− 2 B,m J) 2 Z)
G(m 2 A,m 2 B,m 2 Z)
Ω DM h 2 = C T 3 0
Ω DM h 2 =0.106 ± 0.008
1
CMBR temp
M 3 Pl
1
〈σv〉
Ω DM h 2 =0.106 ± 0.008
〈σv〉 = α2
H(m 2 A,m 2 B,m 2 ⎛
( t = I )
Z)
+ J −⎜ Q, G0⎞ ⎟r = Q 2 − 2Q(I + J)+(I − J) 2
m 2