Inflationary Parameters in Renormalization Group Improved $\phi^4$ Theory

TL;DR

This paper investigates how quantum corrections via the renormalization group affect inflationary parameters in a scalar $ ext{phi}^4$ theory with scalar-curvature interactions, aligning theoretical predictions with cosmological observations.

Contribution

It introduces a detailed numerical analysis of inflationary parameters considering quantum corrections in a $ ext{phi}^4$ model with scalar-curvature coupling, highlighting the impact of RG running.

Findings

RG running induces non-universal contributions to $n_s$ and $r$.

Quantum corrections can increase the tensor-to-scalar ratio $r$.

Planck data is compatible with the $ ext{phi}^4$ theory with finite scalar-curvature coupling.

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.