The Curvature Perturbation in the Axion-type Curvaton Model

Abstract

We study the axion-type curvaton model, with emphasis on the large field regime where analytic results are very difficult to obtain. We evaluate the tensor-scalar ratio $r$ using WMAP normalization and the non-linearity parameters $f_{NL}$ and $g_{NL}$ by solving the equations numerically using the $δN$ formalism. We compare them with results for the curvaton with quadratic potential. We find that $r$ is much smaller for the axion-type case compared to the result from the quadratic potential, with the difference increasingly more pronounced at larger field values. $g_{NL}$ is found to be positive, unlike the quadratic case where it is negative, and the amplitude of $g_{NL}$ is much larger. Moreover, there is a nearly linear scaling between $g_{NL}$ and $f_{NL}$, with small deviation from linearity at large field values. The slope between $g_{NL}$ and $f_{NL}$ depends on the parameters characterizing the axion-type curvaton model. We further consider a mixed scenario where both the inflaton and the curvaton contribute to the primordial power spectrum and the non-Gaussianity parameters are found to be much larger than those in the case with quadratic potential.