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The previous proposal (by two of us) of chain inflation with the QCD axion isshown to fail. The proposal involved a series of fast tunneling events, yethere it is shown that tunneling is too slow. We calculate the bubble nucleationrates for phase transitions in the thick wall limit, approximating the barrierby a triangle. A similar problem arises in realization of chain inflation inthe string landscape that uses series of minima along the monodromy staircasearound the conifold point. The basic problem is that the minima of thepotential are too far apart to allow rapid enough tunneling in these twomodels. We entertain the possibility of overcoming this problem by modifyingthe gravity sector to a Brans-Dicke theory. However, one would need extremelysmall values for the Brans-Dicke parameter. Many successful alternatives exist,including other "axions" (with mass scales not set by QCD) or potentials withcomparable heights and widths that do not suffer from the problem of slowtunneling and provide successful candidates for chain inflation.

Slow nucleation rates in Chain Inflation with QCD Axions or Monodromy