Tensor to Scalar Ratio in Non-Minimal $ϕ^4$ Inflation

Abstract

We reconsider non-minimal λϕ^4 chaotic inflation which includes the gravitational coupling term ξ\mathcal{R} ϕ^2, where ϕdenotes a gauge singlet inflaton field and \mathcal{R} is the Ricci scalar. For ξ>> 1 we require, following recent discussions, that the energy scale λ^{1/4} m_P / \sqrtξ for inflation should not exceed the effective UV cut-off scale m_P / ξ, where m_P denotes the reduced Planck scale. The predictions for the tensor to scalar ratio r and the scalar spectral index n_s are found to lie within the WMAP 1-σbounds for 10^{-12} < λ< 10^{-4} and 10^{-3} < ξ< 10^2. In contrast, the corresponding predictions of minimal λϕ^4 chaotic inflation lie outside the WMAP 2-σbounds. We also find that r > 0.002, provided the scalar spectral index n_s > 0.96. In estimating the lower bound on r we take into account possible modifications due to quantum corrections of the tree level inflationary potential.