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

Abstract

We reconsider non-minimal \lambda \phi^4 chaotic inflation which includes the gravitational coupling term \xi \mathcal{R} \phi^2, where \phi denotes a gauge singlet inflaton field and \mathcal{R} is the Ricci scalar. For \xi >> 1 we require, following recent discussions, that the energy scale \lambda^{1/4} m_P / \sqrt{\xi} for inflation should not exceed the effective UV cut-off scale m_P / \xi, 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-\sigma bounds for 10^{-12} < \lambda < 10^{-4} and 10^{-3} < \xi < 10^2. In contrast, the corresponding predictions of minimal \lambda \phi^4 chaotic inflation lie outside the WMAP 2-\sigma bounds. 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.