Minimal inflationary cosmologies and constraints on reheating

With the growing consensus on simple power law inflation models not being favored by the PLANCK observation, dynamics for the non-standard form of the inflaton potential gain significant interest in the recent past. In this paper, we analyze in great detail classes of phenomenologically motivated inflationary models with non-polynomial potential which are the generalization of the potential introduced in \cite{mhiggs}. After the end of inflation, inflaton field will coherently oscillate around its minimum. Depending upon the initial amplitude of the oscillation and coupling parameters standard parametric resonance phenomena will occur. Therefore, we will study how the inflationary model parameters play an important role in understanding the resonant structure of our model under study. Subsequently, the universe will go through the perturbative reheating phase. However, without any specific model consideration, we further study the constraints on our models based on model independent reheating constraint analysis.