k-inflation: non-separable case meets ACT measurements

We investigate a non-separable subset ofk-essence in which the kinetic and potential sectors interact through anX ^ρ V(ϕ) coupling, implemented via a potential-dependent prefactorf(ϕ) = 1+2KV. In slow roll, this structure preserves a constant sound speedc _s ²= 1/(2ρ- 1) while modifying the Hubble flow in a controlled way, thereby shifting the inflationary observables relative to the separable template. For monomial potentialsV=Aϕⁿ (withn= 2 andn= 2/3 as representative cases) we derive closed analytic expressions forn _s (N _∗) andr(N _∗) toO(ϵ _mix²), whereϵ _mix∝Kencodes the non-separableX ^ρ Vmixing, and we validate them against exact background integrations. The analytic and numerical predictions agree at the sub-per-mille level forn_s and at the percent level forr, confirming the accuracy of the small-mixing expansion. ForK< 0 the mixing systematically lowers bothn_s andrat fixedN _∗, allowing otherwise marginal monomials to fall within the region favored by recent ACT+Planck+BAO constraints (P-ACT-LB). All solutions shown satisfy the health conditionf(ϕ) > 0 and the positivity boundV< 1/(2|K|) (fromf> 0). We also discuss parameter dependence and the expected equilateral-type non-Gaussianity, which remains comfortably within current bounds for the benchmarks considered.