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The inflationary dynamics and preheating in a model with a non-minimallycoupled inflaton field in the metric and Palatini formalisms are studied inthis paper. We find that in both formalisms, irrespective of the initialconditions, our Universe will evolve into a slow-roll inflationary era and thenthe scalar field rolls into an oscillating phase. The value of the scalar fieldat the end of the inflation in the Palatini formalism is always larger thanthat in the metric one, which becomes more and more obvious with the increaseof the absolute value of the coupling parameter $|\xi|$. During the preheating,we find that the inflaton quanta are produced explosively due to the parameterresonance and the growth of inflaton quanta will be terminated by thebackreaction. With the increase of $|\xi|$, the resonance bands gradually closeto the zero momentum ($k=0$), and the structure of resonance changes andbecomes broader and broader in the metric formalism, while, it remains to benarrow in the Palatini formalism. The energy transfer from the inflaton fieldto the fluctuation becomes more and more efficient with the increase of$|\xi|$, and in the metric formalism the growth of the efficiency of energytransfer is much faster than that in the Palatini formalism. Therefore, theinflation and preheating show different characteristics in differentformalisms.

Inflationary dynamics and preheating of the non-minimally coupled inflaton field in the metric and Palatini formalisms