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It is known that the no-boundary proposal in the traditional Einstein gravitydoes not prefer inflation, that is, the probability of realizing a large numberof e-folds is exponentially suppressed. This situation may be changeddrastically in a class of nonlinear massive gravity theories recently proposedby deRham, Gabadadze and Tolley, called dRGT massive gravity. We show that thecontribution from the massive gravity sector can enhance the probability of alarge number of e-folds substantially for a sufficiently large mass parametermg comparable to the Hubble parameter during inflation, say $m_g \gtrsim10^{12}$ GeV. We illustrate possible models to trigger such a large massparameter in the early universe while it is negligibly small in the presentuniverse. This opens a new window to explore the inflationary scenario in thecontext of quantum cosmology.

Hartle-Hawking no-boundary proposal in dRGT massive gravity: Making inflation exponentially more probable