Inflationary parameters in renormalization group improved ϕ4 theory

Abstract

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.