# Generalized surface tension bounds in vacuum decay

## Abstract

Coleman and De Luccia (CDL) showed that gravitational effects can prevent the decay by bubble nucleation of a Minkowski or AdS false vacuum. In their thin-wall approximation this happens whenever the surface tension in the bubble wall exceeds an upper bound proportional to the difference of the square roots of the true and false vacuum energy densities. Recently it was shown that there is another type of thin-wall regime that differs from that of CDL in that the radius of curvature grows substantially as one moves through the wall. Not only does the CDL derivation of the bound fail in this case, but also its very formulation becomes ambiguous because the surface tension is not well defined. We propose a definition of the surface tension and show that it obeys a bound similar in form to that of the CDL case. We then show that both thin-wall bounds are special cases of a more general bound that is satisfied for all bounce solutions with Minkowski or AdS false vacua. We discuss the limit where the parameters of the theory attain critical values and the bound is saturated. The bounce solution then disappears and a static planar domain wall solution appearsmore »

- Authors:

- Publication Date:

- Research Org.:
- Columbia Univ., New York, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1422864

- Alternate Identifier(s):
- OSTI ID: 1503891

- Grant/Contract Number:
- SC0011941

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Masoumi, Ali, Paban, Sonia, and Weinberg, Erick J. Generalized surface tension bounds in vacuum decay. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.045017.
```

```
Masoumi, Ali, Paban, Sonia, & Weinberg, Erick J. Generalized surface tension bounds in vacuum decay. United States. doi:10.1103/PhysRevD.97.045017.
```

```
Masoumi, Ali, Paban, Sonia, and Weinberg, Erick J. Tue .
"Generalized surface tension bounds in vacuum decay". United States. doi:10.1103/PhysRevD.97.045017.
```

```
@article{osti_1422864,
```

title = {Generalized surface tension bounds in vacuum decay},

author = {Masoumi, Ali and Paban, Sonia and Weinberg, Erick J.},

abstractNote = {Coleman and De Luccia (CDL) showed that gravitational effects can prevent the decay by bubble nucleation of a Minkowski or AdS false vacuum. In their thin-wall approximation this happens whenever the surface tension in the bubble wall exceeds an upper bound proportional to the difference of the square roots of the true and false vacuum energy densities. Recently it was shown that there is another type of thin-wall regime that differs from that of CDL in that the radius of curvature grows substantially as one moves through the wall. Not only does the CDL derivation of the bound fail in this case, but also its very formulation becomes ambiguous because the surface tension is not well defined. We propose a definition of the surface tension and show that it obeys a bound similar in form to that of the CDL case. We then show that both thin-wall bounds are special cases of a more general bound that is satisfied for all bounce solutions with Minkowski or AdS false vacua. We discuss the limit where the parameters of the theory attain critical values and the bound is saturated. The bounce solution then disappears and a static planar domain wall solution appears in its stead. The scalar field potential then is of the form expected in supergravity, but this is only guaranteed along the trajectory in field space traced out by the bounce.},

doi = {10.1103/PhysRevD.97.045017},

journal = {Physical Review D},

number = 4,

volume = 97,

place = {United States},

year = {2018},

month = {2}

}

DOI: 10.1103/PhysRevD.97.045017

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