Consistency relation for single scalar inflation

TL;DR

This work extends single-field inflation to a general Lagrangian $L(\xi,\phi)$ and derives a generalized consistency relation $P_T/P_S = -8 c_s^2 n_T$, where $c_s^2 = {\cal L}_{\xi}/({\cal L}_{\xi}+2\xi{\cal L}_{\xi\xi})$, highlighting how a non-quadratic kinetic term affects non-Gaussianity. The curvature bispectrum is shown to depend on two dimensionless amplitudes; one is expressible via $c_s$ and standard observables, enabling a direct observational test, while the second provides a cross-check. An explicit form for the dimensionless bispectrum $f(k_1,k_2,k_3)$ is given, with amplitudes $f_1$ and $f_2$ tied to $c_s$ and higher-derivative couplings, reproducing prior results in appropriate limits and vanishing for degenerate triangles as $k_3^2$. Overall, the paper provides a concrete, testable signature of non-quadratic kinetic terms in single-field inflation and a robust internal consistency framework.

Abstract

Single scalar field inflation with a generic, non-quadratic in derivatives, field Lagrangian is considered. It is shown that non-Gaussianity of curvature perturbations is characterized by two dimensionless amplitudes. One of these amplitudes can be expressed in terms of the usual inflationary observables -- the scalar power, the tensor power, and the tensor index. This consistency relation provides an observational test for the single scalar inflation.