Theory T3
English (Official)
ρ
R R(t)
s
a(t) R(t) = a(t)R
s
a˙ 2 kc2
( a ) = A 1 ρ(t) − R2a2(t)
s
k c
page 1 of 5
Theory T3
English (Official)
A
1
2
ρ(t)c
ρ˙ + A 2 (ρ + ( c p 2 )) a a ˙ = 0
here p denotes the pressure on the
sphere.
A
2
p = p(ρ)
p(t)/c2
= wρ(t) w
H =a˙/a
t 0 ρ 0 H 0 a 0 a 0 = 1
w
k = 0 a(t)
a(t = 0) = 0 a = 1
0
k k = +1
k = 0 k = −1
2 2
Ω = ρ/ρ ρ c =H /A
c c 1
A
1
page 2 of 5
Theory T3
English (Official)
k Ω H a R 0
Ω k = +1 k = 0 k = −1
(Ω(t) − 1)
(Ω(t) − 1)
(Ω(t) − 1) ≪ 1.
(a¨ > 0)
−1
(d(aH) /dt < 0)
ϵ = −H˙ /H 2 ϵ < 1
ϵ < 1 ϵ = 1 N
dN = dlna = Hdt N = 0
ϕ(t)
ϕ¨ +3Hϕ˙
=
−V′
′ ∂V
V = V(ϕ) V =
∂ϕ
page 3 of 5
Theory T3
English (Official)
H2 = 1 1ϕ˙2 +V
3M
p
2
l
[2 ]
Mpl
V ϕ ˙2 /2 ϕ ¨
¨ ˙
ϵ η = δ + ϵ δ = −ϕ/(Hϕ)
V
ϵ η dN/dϕ V(ϕ)
V
′ ″
V V
page 4 of 5
Theory T3
English (Official)
n
s
± r r = 16ϵ n = 1 + 2η − 6ϵ ϕ =ϕ
s V start
4 ϕ n
V(ϕ) =Λ n Λ
(Mpl )
ϕ
end
r n n
s
n r n N
s
page 5 of 5