Non-Gaussianity in the modulated reheating scenario

TL;DR

The paper investigates how spatial fluctuations of the inflaton decay rate in a multi-field modulated reheating scenario generate primordial curvature perturbations and accompanying non-Gaussianity. Using the δN formalism, it derives analytic expressions for the power spectrum, bispectrum, and trispectrum, showing that the leading non-Gaussianity arises from super-horizon evolution and giving explicit formulas for $f_{NL}$, $\tau_{NL}$, and $g_{NL}$. A key result is a general inequality $\tau_{NL} \ge \tfrac{36}{25} f_{NL}^2$ and a predictive relation between $f_{NL}$ and $g_{NL}$ in the limit of small intrinsic non-Gaussianity, with $g_{NL}$ comparable to or larger than $f_{NL}$ depending on the ratio $x=Γ/H_0$. These findings provide concrete signatures for distinguishing modulated reheating from other inflationary scenarios with upcoming observations such as Planck.

Abstract

We investigate the non-Gaussianity of primordial curvature perturbation in the modulated reheating scenario where the primordial perturbation is generated due to the spacial fluctuation of the inflaton decay rate to radiation. We use the $δN$ formalism to evaluate the trispectrum of curvature perturbation as well as its bispectrum. We give expressions for three non-linear parameters $f_{NL}, τ_{NL}$ and $g_{NL}$ in the modulated reheating scenario. If the intrinsic non-Gaussianity of scalar field fluctuations and third derivative of the decay rate with respect to scalar fields are negligibly small, $g_{NL}$ has at least the same order of magnitude as $f_{NL}$. We also give general inequality between $f_{NL}$ and $τ_{NL}$ which is true for other inflationary scenarios as long as primordial non-Gaussianity comes from super-horizon evolution.

Figures (3)

• Figure 1: Plot of $Q(x)$ calculated numerically. The fitting formula $Q_{\rm fit}(x)$ lies within the solid line.
• Figure 2: Plot of $Q"(x)/Q'^2(x)$.
• Figure 3: Plot of $Q"'(x)/Q'^3(x)$.