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Inflaton decay and reheating in nonminimal derivative coupling

We investigate the inflaton decay and reheating period after the end of inflation in the non-minimal derivative coupling (NDC) model with chaotic potential. In general, this model is known to provide an enhanced slow-roll inflation caused by gravitationally enhanced friction. We find violent oscillations of Hubble parameter which induces oscillations of the sound speed squared, implying the Lagrangian instability of curvature perturbation $ζ$ under the comoving gauge $φ=0$. Also, it is shown that the curvature perturbation blows up at $\dotϕ=0$, leading to the breakdown of the comoving gauge at $\dotϕ=0$. Therefore, we use the Newtonian gauge to perform the perturbation analysis where the Newtonian potential is employed as a physical variable. The curvature perturbation is not considered as a physical variable which describes a relevant perturbation during reheating.