The false vacuum bubble : - formation and evolution - in collaboration with Bum-Hoon Lee, Chul H. Lee, Siyong Nam, and Chanyong Park Based on PRD74, (2006), PRD75, (2007), arXiv: [hep-th] Wonwoo Lee Sogang University HaengDang Symposium Recent Studies in Astro-Particle Physics - Nov. 30.(Fri.) 2007

The plan of this talk  Motivations, 2. False vacuum bubble nucleation due to a nonminimally coupled scalar field 1) Numerical calculation 2) Thin-wall approximation  The dynamics of a false vacuum bubble : the junction equations 4. Summary and discussions

1. Motivations -I What is the origin of our universe? 1) Is our universe created from nothing? 2) Is our universe created from something? 3) Can the universe create itself?

1. Motivations -II (1) What did the spacetime look like in the very early universe? - Wheeler’s spacetime foam structure - The cosmological constant as a dynamical variable Can we obtain the mechanism for the nucleation of a false vacuum bubble? Can a false vacuum bubble expand within the true vacuum background? (2) The idea of the string theory landscape has a vast number of metastable vacua. Which mechanism worked to select our universe in this landscape? Can we be in the vacuum with positive cosmological constant ? (through an alternative way to KKLT, for example)

2. The Einstein theory of gravity with a nonminimally coupled scalar field Vacuum-to-vacuum phase transition rate Action Einstein equations

curvature scalar Potential Rotationally invariant Euclidean metric : O(4)-symmetry The Euclidean field equations boundary conditions

Our main idea (during the phase transition)

1) Numerical calculation (Case 1) from de Sitter to de Sitter

(Case 2) from flat to de Sitter

(Case 3) from anti-de Sitter to de Sitter

(Case 4) from anti-de Sitter to flat

(Case 5) from anti-de Sitter to anti-de Sitter

False-to-trueTrue-to-false De Sitter – de Sitter OO Flat – de Sitter OO Anti-de Sitter – de Sitter OO Anti-de Sitter – flat OO Anti-de Sitter – Anti- de Sitter OO

2)Thin-wall approximation B is the difference In this approximation Outside the wall

In the wall where inside the wall

(a) false vacuum bubble nucleation if

The coefficient B (b) true vacuum bubble nucleation

The coefficient B if (by S. Parke) where

Two types related to this formalism (1) Boundary surface (2) Surface layer In this case it is related to the discontinuity of the extrinsic curvature of the surface. We consider thin-wall partitions bulk spacetime into two distinct manifolds and with boundaries and, respectively. To obtain the single glued manifold we demand that the boundaries are identified as follows: 3. The dynamics of a false vacuum bubble : the junction equations

We consider the action where In this framework, junction condition becomes or where, a effective negative tension of the wall There are parameter regions including that both and are positive in all ranges of

After squaring twice, the equation turns out to be where the effective potential is with

(1) M = 0 DS – DS

DS – FLAT

DS – ADS

(2) M > 0 DS – SDS

DS – S

DS – SADS

4. Summary and Discussions The false vacuum bubble can be nucleated within the true vacuum background with a nonminimally coupled scalar field expect the phenomenon be possible in many other theories of gravity with similar terms. A false vacuum bubble with minimal coupling, without singularity in their past, can expand within the true vacuum background with nonminimal coupling. An expanding false vacuum bubble is not inside the horizon of a black hole from outside observer’s point of view. Can it be a model for the accelerating expanding universe?

Thank you for your attention!