Multi-chaotic inflation with and without spectator field

Abstract Motivated by the result of Planck+BICEP/Keck recently released, we investigate consistency multi-field inflation models in terms spectral index n s and tensor-to-scalar ratio r . In this study, focus on double-inflaton with without a spectator field. We find that inflaton quadratic potential can become viable when three fields specific hierarchical mass spectrum are realized such two act as inflatons other one is spectator. also discuss conditions to avoid fine-tuning, careful study how prediction depends background trajectory inflaton-field space.