 
Summary: Volume 171, number 2,3 PHYSICSLETTERS B 24 April 1986
STABILITY AND INSTABILITY OF SCALAR FIELDS COUPLED TO GRAVITY
QHan PARK 1 and L.F. ABBOTT 1,2
Physics Department, Brandeis University, Waltham, MA 02254, USA
Received 16 January 1986
We relate the stability criteria of Boucher for a scalar field coupled to gravity to the semiclassicaltunnelling calculations of
Coleman and DeLuccia. This enables us to prove that the Boucherconditions imply both stability when they are satisfied and
instability when they are not. In addition, it provides physical insight into the nature of the Boucher conditions and indicates
that the O(4)invariant, thinwall approximation used in semiclassicaltunnelling computations is reliable.
Consider an extremum_point ¢ = ~_of a scalar po
tential V(g})such that V'(O) = 0. If V(¢) <~0, gravita
tional effects can stabilize the configuration ~ = ¢
even if it is unstable in the absence of gravity [16].
The stability of a given configuration can best be
established by usin_gthe criteria of Boucher [1]. The
configuration ¢ = ¢ is stable if there exists a real func
tion f(¢) satisfying the boundary condition
f(~) = [V(~)/3g] 1/2 (1)
at the point q~= ~ and the differential equation
2(f') 2  3rf 2 = V (2)
