VACUUM DECAY
[56] "Vacuum Instability and Higgs Scalar Mass" by P.H. Frampton.
Phys. Rev. Lett. 37 1378 (1976).
This paper on unstable vacuum decay originated in a course on quantum field theory
I taught in the Department of Physics and Astronomy at the University of California,
Los Angeles (UCLA) in Spring 1976. A question arose around February 1976 from a
student as what to do when the potential has a local minimium which is not a global
minimum? A follow-up question was much more difficult to answer. What is the
lifetime for this unstable vacuum decay? It was immediately obvious that the situation
was analogous to the physics of a boiling liquid and bubble formation. I recalled
the work of James Langer in Ann. Phys. 41, 108 (1967) and 54, 258 (1969).
The correct method to consider a spherical expanding bubble expanding at the speed of
light came to me around April 1976. Because that concept is Lorentz invariant, special
relativity can relate the lifetime to the critical radius.
The critical radius, as in the
case of Langer, follows from the surface tension
(here related to the tunneling amplitude)
and the energy density (depending on the difference in energy
density between the two
vacua).
The two key
ideas in my paper were to treat the vacuum as a material medium
and that
a sphere expanding at the speed of light
appears the same to all inertial observers.
In a
scalar potential my calculation involved technically
the use of an instanton solution. My
original calculation assumed a thin-wall calculation.
Somewhat later others repeated my
calculation numerically
to avoid that assumption but arrived at similar results.
The bubble expanding at the speed of light could possibly
be seeded by a high-energy
collision leading to a doomsday scenario
where the Earth would disappear in less than
one second. This was
mentioned explicitly in paper [56] but was revisited many years
later by other authors unaware of my paper. Back in 1976, Gerard 't Hooft
in some
plenary talks in international conferences called my discovery the
"Frampton Disaster".
At the time in Spring 1976 I considered whether the Big Bang itself
could be an example
of unstable vacuum decay?
I knew that it could solve the horizon problem that the 40,000
or so causally-disconnected regions of the surface of last scattering
were all at a common
temperature. But there was no reason
why the global minimum should be at zero energy
and solve
the cosmological problem. I published nothing in 1976 about relating vacuum
decay
to the Big Bang because only one problem was solved, the
horizon problem, and
the other problem of the cosmological
constant remained.
Five years later in 1981
inflationary cosmology was invented by Alan Guth then
improved
upon by Andrei Linde and by Andreas Albrecht and Paul Steinhardt. It
has remained popular.
Inflation is based
on the unstable vacuum decay
and its popularity from 1981 on stemmed
from solving three problems, not one.
The three problems are the horizon problem (which
I knew in 1976), the flatness
problem and the monopole problem (both of which were
unknown to me in 1976).
It is curious that although inflation fails to solve the cosmological
constant
problem, which made me hesitate in 1976, the theoretical cosmology
community is
so delighted to solve three
other cosmological problems it can overlook this unsolved issue.
Vacuum decay plays a role in a possible explanation from string theory of the
value of the cosmological constant by Raphael Busso and Joseph Polchinski
(JHEP 0006 (2000) 006). The small value arises from the gigantic number of minima
in the string landscape which necessarily includes values in the observed range.
The arrival at a tiny positive value uses an anthropic argument of Steven Weinberg
(Phys. Rev. Lett. 59, 2607 (1987)).
The paper [56] introduced a connection between field theory and cosmology which
has remained as a part of mainstream research ever since.
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