Non-minimally Coupled Scalar $k$-Inflation Dynamics

Understand

In this work we shall study $k$-inflation theories with non-minimal coupling of the scalar field to gravity, in the presence of only a higher order kinetic term of the form $\sim \mathrm{const}\times X^{\mu}$, with $X=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi$.

• The study will be focused in the cases where a scalar potential is included or is absent, and the evolution of the scalar field will be assumed to satisfy the slow-roll or the constant-roll condition.
• In the case of the slow-roll models with scalar potential, we shall calculate the slow-roll indices, and the corresponding observational indices of the theory, and we demonstrate that the resulting theory is compatible with the latest Planck data.
• The same results are obtained in the constant-roll case, at least in the presence of a scalar potential.