New features in the curvaton model

We demonstrate novel features in the behavior of the second- and third-order nonlinearity parameters of the curvature perturbation, namely $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$, arising from nonlinear motion of the curvaton field. We investigate two classes of potentials for the curvaton—the first has tiny oscillations superimposed upon the quadratic potential. The second is characterized by a single “feature” separating two quadratic regimes with different mass scales. The feature may either be a bump or a flattening of the potential. In the case of the oscillatory potential, we find that, as the width and height of superimposed oscillations increase, both $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ deviate strongly from their expected values from a quadratic potential. $f_{\mathrm{NL}}$ changes sign from positive to negative as the oscillations in the potential become more prominent. Hence, this model can be severely constrained by convincing evidence from observations that $f_{\mathrm{NL}}$ is positive. $g_{\mathrm{NL}}$, on the other hand, acquires very large negative values. Further, this model can give rise to a large running of $f_{\mathrm{NL}}$, with respect to scale. For the single-feature potential, we find that $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ exhibit oscillatory behavior as a function of the parameter that controls the feature. The running of $f_{\mathrm{NL}}$ with respect to scale is found to be small.

Figure 1

The washboard curvaton potential given by Eq. (29) is shown on the top panel for visual comparison with the corresponding quadratic one. The parameter values are $ϵ=5\times {10}^{-4}$ and $\delta ={10}^{-2}$. We have chosen a large value of $ϵ$ in order to make the oscillations clearly visible. The bottom panel shows the curvaton oscillations about the potential minimum for the quadratic and washboard cases, with the same initial field value given by ${\sigma }_{*}/M_p=0.1$. The parameter values for this plot are $ϵ={10}^{-4}$ and $\delta ={10}^{-2}$.

Figure 2

$f_{\mathrm{NL}}$, $g_{\mathrm{NL}}$, and $n_{f_{\mathrm{NL}}}{f}_{\mathrm{NL}}/{\eta }_{mm}$ are shown as functions of $ϵ$ for the washboard potential, for fixed values of $\delta$, $\Gamma /m$, and ${\sigma }_{*}/M_p$. We have shown plots for two different values of $\Gamma /m$ in order to demonstrate the systematic variation as we change $\Gamma /m$.

Figure 3

Same as Fig. 2, but for two different values of $\delta$, with $\Gamma /m$ and ${\sigma }_{*}/M_p$ kept fixed.

Figure 4

$g_{\mathrm{NL}}$ versus $f_{\mathrm{NL}}$ at different values of $ϵ$ for the washboard potential. The other parameter values are $\Gamma /m={10}^{-2}$, ${\sigma }_{*}/M_p=0.1$, and $\delta ={10}^{-2}$.

Figure 5

The single-feature curvaton potential given by Eq. (34) is shown on the left panel for comparison with the corresponding quadratic one. $d$ is fixed to be 0.1, and we have plotted for $c=2$ and $-1$ to show how the nature of the feature changes with the sign of $c$. The right panel shows the corresponding curvaton oscillations about the potential minimum, with the same initial field value given by ${\sigma }_{*}/M_p=0.1$.

Figure 6

$f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ are shown as functions of $c$ for the single-feature potential, with $d$, $\Gamma /m$, and ${\sigma }_{*}/M_p$ kept fixed.

Figure 7

$g_{\mathrm{NL}}$ versus $f_{\mathrm{NL}}$ at different values of $c$ for the single-feature potential. The other parameter values are $\Gamma /m={10}^{-2}$, ${\sigma }_{*}/M_p=0.1$, and $d=0.1$.