Curvaton with Polynomial Potential

TL;DR

The paper investigates how a curvaton with a polynomial potential shapes the primordial curvature perturbation and local-type non-Gaussianity. It develops a $\delta N$ formalism framework to compute the power spectrum $P_\zeta$ and higher-order non-Gaussianity parameters ($f_{NL}$, $g_{NL}$, $\tau_{NL}$) across regimes where the curvaton’s self-interactions either dominate or are subdominant during inflation. It provides analytic expressions for $P_\zeta$ and the non-Gaussianity parameters in the mass-dominated regime and analyzes how the self-interaction affects red-tilted spectra, the enhancement of higher-order non-Gaussianities, and the viability of mixed inflaton-curvaton scenarios under observational constraints. The results highlight that self-interactions can yield sizable $g_{NL}$ and related observables, offering avenues to constrain model parameters (e.g., $\Omega_{\sigma,D}$, $\lambda$, $\beta$, etc.) with current and upcoming CMB data (e.g., Planck).

Abstract

In general a weakly self-interacting curvaton field is expected and the curvaton potential takes the polynomial form. The curvaton potential can be dominated by the self-interaction term during the period of inflation if the curvaton field stays at a large vacuum expectation value. We use the $δ{\cal N}$ formalism to calculate the primordial curvature perturbation in the various possible scenarios which make the curvaton model much richer.