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 **Bubble**s

(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) **Bubble**s

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 = −

stanton formalism, give approximate analytic

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 limit, have static domain walls

∫ ∫

e stationary points of the potential 3 ; we also

σ = i

action becomes infinite, requiring an infinite instanton

ability.

ve discovered this fact independently [2].

vetic et. al. on singular domain walls **and** their relation

∫

dtp ˙q = i

Ψ 1

= e−σ 1/¯h

d 4 x √ gV (φ(x)) (12)

d 4 x √ gV (φ(x turnpt )) (13)

dt [L E − L turnpt ] (14)

= e −S E/¯h

(15)