Inflationary universe from perfect fluid and $F(R)$ gravity and its
  comparison with observational data
  We investigate the descriptions for the observables of inflationary models,
in particular, the spectral index of curvature perturbations, the
tensor-to-scalar ratio, and the running of the spectral index, in the framework
of perfect fluid models and $F(R)$ gravity theories through the reconstruction
methods. Furthermore, the perfect fluid and $F(R)$ gravity descriptions of
inflation are compared with the recent cosmological observations such as the
Planck satellite and BICEP2 experiment. It is demonstrated with explicit
examples that perfect fluid may lead to the inflationary universe consistent
with the Planck data. It is also shown that several $F(R)$ gravity models,
especially, a power-law model gives the best fit values compatible with the
spectral index and tensor-to-scalar ratio within the allowed ranges suggested
by the Planck and BICEP2 results.
