Primordial non-gaussianities in single field inflation

TL;DR

<p>We address primordial non-Gaussianities in single-field inflation with a general Lagrangian $P(X,\phi)$ by deriving the tree-level three-point function of the comoving curvature perturbation $\mathcal{R}$ using the ADM formalism and an in-in path-integral approach. The analysis extends the Maldacena framework to models with a nontrivial kinetic structure and a generally evolving sound speed $c_s$, introducing the slow-roll-like parameters $\varepsilon$, $\eta$ along with the kinetic-structure parameter $\varepsilon_X$, the sound-speed deviation $u=1-1/c_s^2$, and its rate of change $s$. The principal result is a closed expression for $\langle\mathcal{R}(\mathbf{k}_1)\mathcal{R}(\mathbf{k}_2)\mathcal{R}(\mathbf{k}_3)\rangle$ in terms of these parameters, which reduces to Maldacena’s canonical case when $u=s=0$ and obeys the Maldacena consistency condition in the squeezed limit. The findings show that, under slow-roll, the non-Gaussian signal is small, but they also delineate how a reduced sound speed can imprint distinctive momentum (and thus CMB) signatures, providing a diagnostic for non-canonical inflation in future observations.</p>

Abstract

We calculate the three-point function for primordial scalar fluctuations in a single field inflationary scenario where the scalar field Lagrangian is a completely general function of the field and its first derivative. We obtain an explicit expression for the three-point correlation function in a self-consistent approximation scheme where the expansion rate varies slowly, analogous to the slow-roll limit in standard, single-field inflation. The three-point function can be written in terms of the familiar slow-roll parameters and three new parameters which measure the non-trivial kinetic structure of the scalar field, the departure of the sound speed from the speed of light, and the rate of change of the sound speed.