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Summary: Class. Quantum Grav. 4 (1987) L201-L204. Printed in the UK
LETTER TO THE EDITOR
Vacuum decay in curved backgrounds
L F AbbotttS, Diego HarariO and Q-Han Park11
t Physics Department, Boston University, Boston, MA 02215, USA
5 Physics Department, University of Florida, Gainesville, FL 32611, USA
11 Physics Department, Brandeis University, Waltham, MA 02254, USA
Received 24 June 1987
Abstract. We evaluate the effect of gravity on the probability of vacuum decay through
bubble nucleation for a scalar field in an arbitrary curved background up to first order in
an expansion in powers of Rp', where R is the scalar curvature of the background metric
at the location of the bubble and p is the size of the bubble as it would appear in a flat space.
The mechanism by which a scalar field in a false vacuum can decay into its true ground
state is well known [l-31 and many cosmological implications (e.g. inflation, domain
walls, cosmic strings, etc) have been considered. Qualitatively, the decay proceeds
through the materialisation of bubbles of'true vacuum within the false vacuum phase,
which is a quantum tunnelling effect. Once they are formed the bubbles expand,
asymptotically approaching the speed of light.
The probability per unit time and per unit volume for the materialisation of a
bubble, r/V, is given in the semiclassical limit by an expression of the form
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