Scalar Field Assisted $f(R)$ Gravity Inflation
  In this paper we investigate the inflationary dynamics of an $f(R)$ gravity
in the presence of a canonical scalar field. We specifically choose the
cosmological evolution to be a quasi-de Sitter evolution and also the $f(R)$
gravity is assumed to be a modified version of the $R^2$ gravity. We
investigate which scalar field potential can produce the quasi-de Sitter
evolution for the choice of the $f(R)$ gravity we made, and also we study in
detail the inflationary dynamics of the resulting theory. As we demonstrate,
the spectral index is identical to the one corresponding to the ordinary $R^2$
gravity, while the scalar-to-tensor ratio is found to be smaller than the $R^2$
inflation one consequently, compatibility with both the Planck 2015 and
BICEP2/Keck-Array data is achieved.
