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The scenario of the slow-roll inflation is studied in the frame of thescalar-tensor theory of gravity where the scalar field has a non-minimalcoupling to the geometric part. After deriving the main dynamical andperturbation equations, the model is investigated in detail for differentfunctions of the potential and the coupling function. Considering theconsistency of the model with observational model results into specific rangesfor the free constants of the model. Then, the obtained ranges are reconsideredto realize whether they satisfy the swampland criteria. It is found that theswampland criteria impose another limitation and reduce the ranges. Using thefinal outcomes for the free constants of the model, we briefly consider thereheating phase to find out about the number of e-fold for the phase and thereheating temperature.

Revisiting Scalar Tensor inflation by swampland criteria and Reheating