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

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 $f_{\mathrm{NL}},{\tau }_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ 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 $f_{\mathrm{NL}}\sim \mathcal{O}(1)$, 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 $f_{\mathrm{NL}}$ but with a different sign of $g_{\mathrm{NL}}$. This provides a possibility to discriminate these two competitive models by looking at the sign of $g_{\mathrm{NL}}$. 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.

38 pages, 12 figures

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