Bubble Nucleation and Eternal Inflation - cosmo 06

nton is cut along the surface denoted by the black disc, which is

CDL Vacuum **Bubble**s

pact) instanton, like the one found in the absence

≪ 1, **and**

onto x(s = the 0) = x 0 hypersurface indicated (7) in the conformal diagram. The

much ẋ(s faster = s max decay, ) = 0 so that

(8)

this hypersurface specify the initial conditions for the lorentzian

e bubble wall, indicated by the line with an arrow. Depending

l phase, this process describes the nucleation of a true or false

e. The zeros of ρ continue into the forward light cones indicated

E ≃ u

in the decay T,F

rate as V F → 0.

V (φ)

te that while

(9)

(10)

[1] are cor-

Instead 5we

x H

artitioned by

relines.

Minkowski

ss where the

– as argued

here R is the

x F

x T

the false vac- Figure 1: The potential V (φ), with

. The stabilly

metastable

the true vacuum x T , the false vacuum

x F **and** the “Hawking-Moss”

point x H labeled. ∫

ago by Cole-

-wall limit **and** subsequently discussed by several

S I = −

e instanton formalism, give approximate analytic

or of the instanton solutions in the limit where

umerical techniques.

S

After elucidating the actual

argue in Sec. 5 that BG = −

the Great Divide consists

in the V F → 0 limit, have static domain walls

∫ ∫

false stationary points of the potential 3 ; we also

σ = i

ubtraction becomes infinite, requiring an infinite instanton

probability.

t, have discovered this fact independently [2].

of Cvetic et. al. on singular domain walls **and** their relation

∫

dtp ˙q = i

φ (11)

Tunneling = **Bubble** **Nucleation**

d 4 x √ gV (φ(x)) (12)

d 4 x √ gV (φ(x turnpt )) (13)

−σ 1 /¯h

dt [L E − L turnpt ] (14)