T3
Theory
English (Official)
ρ
Rs
a(t)
(
k
ȧ 2
a)
R(t) = a(t)R s
= A1 ρ(t) −
kc 2
R 2s a2 (t)
c
page 1 of 5
R(t)
T3
Theory
English (Official)
A1
ρ(t)c 2
ρ̇ + A2 (ρ + ( c 2 ))
p
ȧ
a
=0
here
sphere.
p
denotes the pressure on the
A2
H = ȧ /a
p = p(ρ)
p(t)/c 2 = wρ(t)
t0 ρ0 H 0 a 0
w
a0 = 1
w
k=0
a(t)
a(t = 0) = 0
k
k=0
A1
a0 = 1
Ω = ρ/ρ c
page 2 of 5
k = −1
ρ c c 2 = H 2/ A 1
k = +1
T3
Theory
English (Official)
k
R0
Ω H a
Ω
k = +1 k = 0
k = −1
(Ω(t) − 1)
(Ω(t) − 1)
(Ω(t) − 1) ≪ 1 .
(ä > 0)
−1
(d(aH ) /dt < 0)
ϵ = −Ḣ /H 2
dN = d ln a = Hdt
ϵ<1
ϵ<1
N=0
ϵ=1
ϕ(t)
ϕ̈ + 3H ϕ̇ = −V ′
V = V(ϕ)
V′ =
∂V
∂ϕ
page 3 of 5
N
T3
Theory
English (Official)
H2 =
Mpl
2
ϕ̇ /2
V
ϵ
1
1 ϕ̇2
+ V]
3M pl2 [ 2
ηV = δ + ϵ
ϵ
V′
ϕ̈
δ = −ϕ̈/(H ϕ̇)
V″
η V dN/dϕ
page 4 of 5
V(ϕ)
T3
Theory
English (Official)
±
r
V(ϕ) = Λ 4 ( Mpl )
ϕ
n
r = 16ϵ
n s = 1 + 2η V − 6ϵ
n
Λ
ϕend
n
r
ns
r
ns
page 5 of 5
N
n
ϕ = ϕ start
ns