We show that inflation with a quadratic potential occurs naturally in theories where an axionlike field mixes with a 4-form. Such an axion is massive, with the mass which arises from the mixing being protected by the axion shift symmetry. The 4-form backgrounds break this symmetry spontaneously and comprise a minilandscape, where their fluxes can change by emission of membranes. Inflation can begin when the 4-form dominates the energy density. Eventually, this energy is reduced by membrane emission, and the axion can roll slowly towards its minimum, as in the simplest version of chaotic inflation.
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Kaloper et al. (2009) studied this question.
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