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.

Figures (10)

• Figure 1: The red (solid), blue (dotted) and green (dashed) lines correspond to the axion potential, quadratic potential and $\theta^2/2-\theta^4/24$ respectively.
• Figure 2: The blue (dashed) line shows the exact value of $f_D$ computed numerically, whereas, the black (dotted) line shows to $f_D$ computed from the analytic approximation in Eq.(\ref{['afd']}), for the quadratic potential.
• Figure 3: The red (solid) line shows $r$ for the cosine potential and the blue (dotted) line for the quadratic potential, respectively, for $\Gamma_{\sigma}/m = 10^{-4}$ and $10^{-5}$. $r$ is seen to decrease as $\Gamma_{\sigma}/m$ decreases.
• Figure 4: Plot of $f_{NL}$. The red (solid), blue (dotted) and green (dashed) lines correspond to axion-type, quadratic and quadratic with $\sigma^4$ correction models, respectively.
• Figure 5: Plot of $g_{NL}$. The red (solid), blue (dotted) and green (dashed) lines correspond to axion-type, quadratic and quadratic with $\sigma^4$ correction models, respectively.