Tilt and Tensor-to-Scalar Ratio in Multi-Scalar Field Inflation: Non-Sum-Separable Case

The canonical multi-scalar field inflation where the kinetic and potential terms are sum-separable is ruled out by the current observations for the chaotic-type potential $V=\sum_{i} \mu_{i} \phi_{i}^{p}$. This paper explores the non-sum-separable case to validate the chaotic-type potential in the multi-scalar field, incorporating a linear coupling term between the kinetic and potential terms in the canonical Lagrangian. This coupling influences the slow-roll parameters and also alters our predictions for the spectral index $n_{s}$ and the tensor-to-scalar ratio $r$, which directly depend on those parameters. In fact, compared to standard canonical multi-field inflation, the values of $n_{s}$ and $r$ decrease to levels consistent with the recent Planck+BICEP/Keck constraint.