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 and which was found in Ref. [1]. We analyze the Lyapunov stability of de Sitter solution and show the stability bound. Calculating the inflationary parameters, we systematically explore the spectral index ns and the tensor-to-scalar ratio r, with varying the four parameters, the scalar-curvature coupling ξ0, the scalar quartic coupling λ0, the renormalization scale μ and the e-folding number N. It is found that the two-loop correction on ns is much larger than the leading-log correction, which has previously been studied in Ref. [2]. We show that the model is consistent with the observation by Planck with WMAP [3,4] and a recent joint analysis of BICEP2 [5]. Keywords: Two-loop effective potential, Spectral index, Tensor-to-scalar ratio