Signatures of Non-Gaussianity in the Curvaton Model

TL;DR

The paper investigates primordial non-Gaussianity in the curvaton model when the curvaton potential includes non-quadratic terms. Using the $ abla N$ formalism, it derives expressions for the bispectrum and trispectrum parameters, showing that $f_{ m NL}$ can be driven to very small values while the trispectrum parameter $g_{ m NL}$ becomes large and negative for small $r$, making the trispectrum a key observable. The authors demonstrate that $g_{ m NL}$ directly measures deviations from a purely quadratic potential, predicting magnitudes around $|g_{ m NL}|\,\sim\,O(10^4)-O(10^5)$ in plausible scenarios, with $ au_{ m NL}$ tied to $f_{ m NL}$ via $ au_{ m NL}=\frac{36}{25} f_{ m NL}^2$. These results imply that future observations, including Planck, could test MSSM-inspired curvaton models by targeting the trispectrum rather than the bispectrum.

Abstract

We discuss the signatures of non-Gaussianity in the curvaton model where the potential includes also a non-quadratic term. In such a case the non-linearity parameter f_NL can become very small, and we show that non-Gaussianity is then encoded in the non-reducible non-linearity parameter g_NL of the trispectrum, which can be very large. Thus the place to look for the non-Gaussianity in the curvaton model may be the trispectrum rather than the bispectrum. We also show that g_NL measures directly the deviation of the curvaton potential from the purely quadratic form. While g_NL depends on the strength of the non-quadratic terms relative to the quadratic one, we find that for reasonable cases roughly g_NL\sim O(-10^4)-O(-10^5), which are values that may well be accessible by future observations.

Figures (4)

• Figure 1: (Left) Plot of $f_{\rm NL}$ as a function of $n$ for several values of $s$. (Right) Plot of $g_{\rm NL}$ as a function of $f_{\rm NL}$ for several values of $s$. Notice that $f_{\rm NL}$ and $n$ have one-to-one correspondence. In both panels, $r=0.01$.
• Figure 2: (Left) Plot of the combination $\sigma_{\rm osc}\sigma^{\prime\prime}_{\rm osc}/\sigma^{\prime 2}_{\rm osc}$ as a function of $n$ for several values of $s$. (Right) Plot of the combination $\sigma_{\rm osc}^2\sigma^{\prime\prime\prime}_{\rm osc}/\sigma^{\prime 3}_{\rm osc}$ as a function of $n$ for several values of $s$.
• Figure 3: Contours of $f_{\rm NL}$ are shown for the case $r=0.01$ in the $n$--$s$ plane. Note that the line of $f_{\rm NL}=0$ is not changed for small values of $r$.
• Figure 4: (Top left) Plot of $-g_{\rm NL}$ as a function of the power $n$ for several values of $s$. The value of $r$ is fixed as $r=0.01$ in the top panels. (Top right) Plot of $-g_{\rm NL}$ as a function of $s$ for several values of the power $n$. (Bottom left) Contours of $g_{\rm NL}$ in the $n$--$r$ plane for the case $s=0.1$. (Bottom right) Contours of $g_{\rm NL}$ in the $n$--$r$ plane for the case $s=0.01$.