Inflationary Parameters in Renormalization Group Improved $\phi^4$
  Theory
  Inflation models can be examined by the cosmological observations, WMAP,
Planck, BICEP2 and so on. These observations directly constrain the spectral
index, $n_s$, and the tensor-to-scalar ratio, $r$. Besides, from a theoretical
point of view, it has been shown that any inflation models asymptote a
universal attractor in $(n_s,r)$ plane for a larger scalar-gravity coupling. In
this work we consider a simple chaotic inflation model with a scalar quartic
and a scalar-curvature interactions. The quantum corrections are introduced for
these interactions through the renormalization group. The inflationary
parameters, $n_s$ and $r$, are numerically calculated with shifting the bare
scalar-gravity coupling $\xi_0$, the quartic scalar bare coupling $\lambda_0$,
the renormalization scale $\mu$ and the e-folding number $N$. The Planck data
is consistent with the $\phi^4$ theory with a finite scalar-curvature coupling.
It is found that the RG running induces a non-universal contribution for $n_s$
and $r$. It can increase the tensor-to-scalar ratio, $r$, which is consistent
with Planck data so that it may approach the BICEP2 data for a small
renormalization scale.
