The Simple Single Field Inflation Models and the Running of Spectral
  Index
  The BICEP2 experiment confirms the existence of primordial gravitational wave
with the tensor-to-scalar ratio $r=0$ ruled out at $7\sigma$ level. The
consistency of this large value of $r$ with the {\em Planck} data requires a
large negative running $n'_s$ of the scalar spectral index. Herein we propose
two types of the single field inflation models with simple potentials to study
the possibility of the consistency of the models with the BICEP2 and {\em
Planck} observations. One type of model suggested herein is realized in the
supergravity model building. These models fail to provide the needed $n'_s$
even though both can fit the tensor-to-scalar ratio and spectral index.
