Generic no-scale inflation inspired from string theory compactifications

Abstract

We propose the generic no-scale inflation inspired from string theory compactifications. We consider the K\"ahler potentials with an inflaton field $\ensuremath{\varphi}$, as well as one, two, and three K\"ahler moduli. Also, we consider the renormalizable superpotential of $\ensuremath{\varphi}$ in general. We study the spectral index and tensor-to-scalar ratio in details, and find the viable parameter spaces which are consistent with the Planck and BICEP/Keck experimental data on the cosmic microwave background (CMB). The spectral index is ${n}_{s}\ensuremath{\simeq}1\ensuremath{-}2/N\ensuremath{\sim}0.965$ for all models, and the tensor-to-scalar ratio $r$ is $r\ensuremath{\simeq}12/{N}^{2}$, $83/{N}^{4}$ and $4/{N}^{2}$ for the one, two and three moduli models, respectively. The particular $r$ for two moduli model comes from the contributions of the non-negligible higher order term in potential. In the three moduli model, the scalar potential is similar to the global supersymmetry, but the K\"ahler potential is different. The E model with $\ensuremath{\alpha}=1$ and T model with $\ensuremath{\alpha}=1/3$ can be realized in the one modulus model and the three moduli model, respectively. Interestingly, the models with quadratic and quartic potentials still satisfy the current tight bound on $r$ after embedding into no-scale supergravity.