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In the thin-wall approximation, the decay of a gravitating false vacuum to alower-energy state is affected by the cosmological horizon structure in bothspaces. The nucleation radius of a bubble of true vacuum depends on the surfacetension of its boundary and equals the false vacuum cosmological horizon at acritical tension. We argue that there is no tunneling instanton solution beyondthe critical tension and argue that there is therefore a bound on allowedmembrane tension in theories which rely on semiclassical tunneling to relax thecosmological constant.

Horizons and Tunneling in the Euclidean False Vacuum