  In the thin-wall approximation, the decay of a gravitating false vacuum to a
lower-energy state is affected by the cosmological horizon structure in both
spaces. The nucleation radius of a bubble of true vacuum depends on the surface
tension of its boundary and equals the false vacuum cosmological horizon at a
critical tension. We argue that there is no tunneling instanton solution beyond
the critical tension and argue that there is therefore a bound on allowed
membrane tension in theories which rely on semiclassical tunneling to relax the
cosmological constant.
