For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.
On the Realization of WIMPflation
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Inflaton Regeneration via Scalar Couplings: Generic Models and the Higgs Portal
For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.