Non-Gaussian Enhancements of Galactic Halo Correlations in Quasi-Single Field Inflation

Abstract

We consider a quasi-single field inflation model in which the inflaton interacts with a massive scalar field called the isocurvaton. Due to the breaking of time translational invariance by the inflaton background, these interactions induce kinetic mixing between the inflaton and isocurvaton, which is parameterized by a constant $\mu$. We derive analytic formulae for the curvature perturbation two-, three-, four-, five-, and six-point functions explicitly in terms of the external wave-vectors in the limit where $\mu$ and the mass of the isocurvaton $m$ are both much smaller than $H$. In previous work, it has been noted that when $m/H$ and $\mu/H$ are small, the non-Gaussianities predicted by quasi-single field inflation give rise to long wavelength enhancements of the power spectrum for biased objects (e.g., galactic halos). We review this calculation, and calculate the analogous enhanced contribution to the bispectrum of biased objects. We determine the scale at which these enhanced terms are larger than the Gaussian piece. We also identify the scaling of these enhanced parts to the $n$-point function of biased objects.