Non-Minimal Two-Loop Inflation

Abstract: We investigate the chaotic inflationary model using the two-loop effective potential of a self-interacting scalar field theory in curved spacetime. We use the potential which contains a non-minimal scalar curvature coupling and a quartic scalar self-interaction. We analyze the Lyapunov stability of de Sitter solution and show the stability bound. Calculating the inflationary parameters, we systematically explore the spectral index $n_s$ and the tensor-to-scalar ratio $r$, with varying the four parameters, the scalar-curvature coupling $\xi_0$, the scalar quartic coupling $\lambda_0$, the renormalization scale $\mu$ and the e-folding number $N$. It is found that the two-loop correction on $n_s$ is much larger than the leading-log correction, which has previously been studied. We show that the model is consistent with the observation by Planck with WMAP and a recent joint analysis of BICEP2.