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.
