Non-minimally coupled scalar k-inflation dynamics

In this work, we shall study k-inflation theories with non-minimal coupling of the scalar field to gravity, in presence only a higher-order kinetic term form $$\sim \hbox {const}\times X^{\mu }$$ , $$X=\frac{1}{2}\partial _{\mu } \phi \partial ^{\mu }\phi $$ . The will be focused cases where potential is included or absent, and evolution assumed satisfy slow-roll constant-roll condition. case models potential, calculate indices corresponding observational theory, demonstrate that resulting theory compatible latest Planck data. same results are obtained case, at least potential. without considered, less appealing since these strongly model dependent, for power-law choice coupling, non-viable. Finally, due fact tensor power spectra conformal invariant quantities, argue Einstein frame counterpart can viable invariance indices. more involved thus difficult work it analytically, so one implication our provide evidence viability another class models.