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.

Figures (6)

• Figure 1: $r$ vs. $n_s$ for the radiatively corrected non-minimal $\phi^4$ potential defined in Eq. (\ref{['ApproxPotential']}) with the number of e-foldings $N_0 = 60$. The WMAP 1-$\sigma$ (68% confidence level) bounds are shown in yellow. Along each curve we vary either $\kappa$ (left panel) or $\xi$ (right panel), keeping one or the other fixed. The black dots represent the meeting points of the hilltop and the $\phi^4$ solutions and correspond, for a given $\xi$, to the maximum value of $\kappa$.
• Figure 2: $n_s$ vs. log$_{10}(\kappa)$ and log$_{10}(\xi)$ for radiatively corrected non-minimal $\phi^4$ inflation with the number of e-foldings $N_0 = 60$.
• Figure 3: $r$ vs. log$_{10}(\kappa)$ and log$_{10}(\xi)$ for radiatively corrected non-minimal $\phi^4$ inflation with the number of e-foldings $N_0 = 60$.
• Figure 4: $V^{1/4}/\Lambda$ and log$_{10}(\lambda)$ vs. log$_{10}(\xi)$ and log$_{10}(\kappa)$ for radiatively-corrected non-minimal $\phi^4$ inflation with the number of e-foldings $N_0 = 60$.
• Figure 5: $r$ vs. $n_s$ (first row) and $n_s$ and $r$ vs. log$_{10}(\xi)$ (second row) for tree level ($\kappa = 0$) non-minimal $\phi^4$ inflation with the number of e-foldings $N_0 = 50$ (red dashed curve) and $N_0 = 60$ (green solid curve). The WMAP 1-$\sigma$ (68% confidence level) bounds are shown in yellow.