Bubble Nucleation and Eternal Inflation - cosmo 06
Bubble Nucleation and Eternal Inflation - cosmo 06
Bubble Nucleation and Eternal Inflation - cosmo 06
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to the hypersurface indicated in the conformal diagram. The<br />
x(s = 0) = x 0 (7)<br />
t) instanton, like the<br />
False<br />
one found in the absence<br />
Vacuum <strong>Bubble</strong>s<br />
(s h faster = s max decay, ) = 0 so that<br />
(8)<br />
his hypersurface specify the initial conditions for the lorentzian<br />
E ≃ u<br />
the decay T,F (9)<br />
bubble<br />
rate as<br />
wall,<br />
V F → 0.<br />
indicated by the line with an arrow. Depending<br />
V (φ) (10)<br />
hat while<br />
phase, this process describes the nucleation of a true or false<br />
] are corstead<br />
The 5we<br />
zeros of xρ H<br />
continue into the forward light cones indicated<br />
itioned by<br />
Lee <strong>and</strong> Weinberg 1987<br />
nes.<br />
Can we tunnel up<br />
inkowski<br />
where the x F<br />
x T<br />
L(ee)W(einberg) <strong>Bubble</strong>s<br />
as argued<br />
R is the<br />
false vache<br />
stabil-<br />
Figure 1: The potential V (φ), φ with<br />
(11)<br />
the true vacuum x T , false vacuum<br />
x F <strong>and</strong> the “Hawking-Moss”<br />
etastable<br />
But, not the only way to make False Vacuum...<br />
point x H labeled. ∫<br />
by Colel<br />
limit <strong>and</strong> subsequently discussed by several<br />
S I = −<br />
FGG Mechanism<br />
stanton formalism, give approximate analytic<br />
Farhi, Guth, Guven 1990<br />
f the instanton solutions in the limit where<br />
rical techniques.<br />
S<br />
After elucidating the actual<br />
ue in Sec. 5 that BG = −<br />
the Great Divide consists<br />
the V F → 0 Hawking-Moss<br />
limit, have static domain walls<br />
∫ ∫<br />
e stationary points of the potential 3 ; we also<br />
σ = i<br />
action becomes infinite, requiring an infinite instanton<br />
ability.<br />
Hawking <strong>and</strong> Moss 1982<br />
ve discovered this fact independently [2].<br />
vetic et. al. on singular domain walls <strong>and</strong> their relation<br />
∫<br />
Instanton<br />
dtp ˙q = i<br />
Ψ 1<br />
= e−σ 1/¯h<br />
d 4 x √ gV (φ(x)) (12)<br />
Thermal Activation<br />
Garriga <strong>and</strong> Megev<strong>and</strong> 2004<br />
Gomberoff et. al. 2004<br />
d 4 x √ gV (φ(x turnpt )) (13)<br />
dt [L E − L turnpt ] (14)<br />
= e −S E/¯h<br />
Stochastic<br />
Fluctuations<br />
Starobinski<br />
Linde<br />
Creation of a<br />
universe from nothing<br />
Vilenkin 1982<br />
(15)