Bubble Nucleation and Eternal Inflation - cosmo 06

to the hypersurface indicated in the conformal diagram. The
x(s = 0) = x 0 (7)
t) instanton, like the
False
one found in the absence
Vacuum Bubbles
(s h faster = s max decay, ) = 0 so that
(8)
his hypersurface specify the initial conditions for the lorentzian
E ≃ u
the decay T,F (9)
bubble
rate as
wall,
V F → 0.
indicated by the line with an arrow. Depending
V (φ) (10)
hat while
phase, this process describes the nucleation of a true or false
] are corstead
The 5we
zeros of xρ H
continue into the forward light cones indicated
itioned by
Lee and Weinberg 1987
nes.
Can we tunnel up
inkowski
where the x F
x T
L(ee)W(einberg) Bubbles
as argued
R is the
false vache
stabil-
Figure 1: The potential V (φ), φ with
(11)
the true vacuum x T , false vacuum
x F and the “Hawking-Moss”
etastable
But, not the only way to make False Vacuum...
point x H labeled. ∫
by Colel
limit and subsequently discussed by several
S I = −
FGG Mechanism
stanton formalism, give approximate analytic
Farhi, Guth, Guven 1990
f the instanton solutions in the limit where
rical techniques.
S
After elucidating the actual
ue in Sec. 5 that BG = −
the Great Divide consists
the V F → 0 Hawking-Moss
limit, have static domain walls
∫ ∫
e stationary points of the potential 3 ; we also
σ = i
action becomes infinite, requiring an infinite instanton
ability.
Hawking and Moss 1982
ve discovered this fact independently [2].
vetic et. al. on singular domain walls and their relation
∫
Instanton
dtp ˙q = i
Ψ 1
= e−σ 1/¯h
d 4 x √ gV (φ(x)) (12)
Thermal Activation
Garriga and Megevand 2004
Gomberoff et. al. 2004
d 4 x √ gV (φ(x turnpt )) (13)
dt [L E − L turnpt ] (14)
= e −S E/¯h
Creation of a
universe from nothing
Vilenkin 1982
(15)