Primordial Curvature Fluctuation and Its Non-Gaussianity in Models with Modulated Reheating

TL;DR

This work analyzes non-Gaussianity in models where reheating is modulated by a modulus field, producing primordial perturbations alongside inflaton fluctuations. Using the $\delta N$ formalism, it derives expressions for $f_{\rm NL}$, $\tau_{\rm NL}$, and $g_{\rm NL}$ and shows that large non-Gaussianity can arise from the non-linear coupling between the decay rate and the modulus, with a distinctive trispectrum signature. A key result is a consistency relation among the non-Gaussian parameters, and a diagnostic based on the sign of $g_{\rm NL}$ that can distinguish modulated reheating from curvaton scenarios. Applying the framework to chaotic inflation (quadratic, quartic+quadratic, and sextic) demonstrates that modulus contributions can reconcile several models with current data by lowering $r$ and adjusting $n_s$, while still permitting observable non-Gaussianity. These findings provide concrete observational handles for testing modulated reheating in upcoming CMB experiments.

Abstract

We investigate non-Gaussianity in the modulated reheating scenario where fluctuations of the decay rate of the inflaton generate adiabatic perturbations, paying particular attention to the non-linearity parameters $f_{\rm NL}, τ_{\rm NL}$ and $g_{\rm NL}$ as well as the scalar spectral index and tensor-to-scalar ratio which characterize the nature of the primordial power spectrum. We also take into account the pre-existing adiabatic perturbations produced from the inflaton fluctuations. It has been known that the non-linearity between the curvature perturbations and the fluctuations of the decay rate can yield non-Gaussianity at the level of $f_{\rm NL} \sim \mathcal{O}(1)$, but we find that the non-linearity between the decay rate and the modulus field which determines the decay rate can generate much greater non-Gaussianity. We also discuss a consistency relation among non-linearity parameters which holds in the scenario and find that the modulated reheating yields a different one from that of the curvaton model. In particular, they both can yield a large positive $f_{\rm NL}$ but with a different sign of $g_{\rm NL}$. This provides a possibility to discriminate these two competitive models by looking at the sign of $g_{\rm NL}$. Furthermore, we work on some concrete inflation models and investigate in what cases models predict the spectral index and the tensor-to-scalar ratio allowed by the current data while generating large non-Gaussianity, which may have many implications for model-buildings of the inflationary universe.

Figures (12)

• Figure 1: The relative error for the function $Q(x)$ between the one obtained by analytic and numerical methods for the cases with the interaction $-y\phi \bar{\psi}\psi$ (red solid line), $-M\phi \chi^2$ (green dashed line) and $-h\phi^2 \chi^2$ (blue dotted line). Here we assumed $V \propto \phi^6$ for the inflaton potential. For the cases with the quadratic potential $V \propto \phi^2$, the errors are smaller than those given in this figure.
• Figure 2: Consistency relations among three non-linearity parameters are shown for the case with modulated reheating corresponding to Eq. \ref{['eq:consistency']} (red solid line) and the curvaton model for the case where the curvaton decays before it dominates the universe corresponding to Eq. (77) in Ref Ichikawa:2008iq (black dashed line). In this figure, the consistency relation is presented as contours of $g_{\rm NL}$ in the $f_{\rm NL}$--$\tau_{\rm NL}$ plane. The line for models with "ungaussiton" Suyama:2008nt is also shown (blue dotted line). For this model, the relation between $f_{\rm NL}$ and $\tau_{\rm NL}$ is given, thus it is irrelevant to the value of $g_{\rm NL}$. Notice that the inequality Eq. \ref{['eq:inequality']} should hold for the above mentioned scenarios. Thus we also show a region violating this inequality with shade.
• Figure 3: Contours of $R$ in the $\sigma$--$M$ plane for the chaotic inflation model with quadratic potential. Left and right panels are for case A ($\alpha = 0.3, \beta =-1$) and case B ($\alpha = 0, \beta =-1$), respectively. In the figure, $M$ and $\sigma$ are shown in units of $M_{\rm pl}$.
• Figure 4:
• Figure 5: Contours of $f_{\rm NL}$ in the $\sigma$--$M$ plane for the chaotic inflation model with quadratic potential. Left (right) panels are for case A (B).