Primordial non-Gaussianity in warm $k$-inflation with nonminimal derivative coupling

Abstract

This paper derives the finite-inertia intrinsic thermal bispectrum in potential-free warm $k$-inflation with nonminimal derivative coupling (NMDC). On a fixed Friedmann--Lema\^ıtre--Robertson--Walker geometry, the complete cubic inflaton action determines the nonlinear stochastic source, encompassing temporal, spatial-gradient, and field-dependent kinetic interactions. The retarded solution captures the full momentum-triangle dependence while retaining unequal-time correlations, whereas its equilateral limit yields the intrinsic nonlinearity parameter. The power spectrum is computed with the same response and Gaussian initial state, thereby fixing the statistical normalization. A complementary local freeze-out reduction makes the interaction coefficients and two geometric shape contributions explicit. Comparison along an evolving near-attractor trajectory indicates that unequal-time finite-inertia propagation is crucial for quantitatively predicting the intrinsic bispectrum. The analysis also derives the slow-roll-suppressed nonlinear $δN$ conversion, together with the Arnowitt--Deser--Misner constraints and cubic vertices that characterize the direct gravitational effects of NMDC. These results clarify the respective roles of local freeze-out estimates and finite-inertia stochastic evolution in the nonlinear prediction.