We consider dark matter production during the inflaton oscillation epoch. It is conceivable that renormalizable interactions between dark matter and inflaton may be negligible. In this case, the leading role is played by higher dimensional operators generated by gravity and thus suppressed by the Planck scale. We focus on dim-6 operators and study the corresponding particle production in perturbative and non-perturbative regimes. We find that the dark matter production rate is dominated by non-derivative operators involving higher powers of the inflaton field. Even if they appear with small Wilson coefficients, such operators can readily account for the correct dark matter abundance.
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