In quasi-single field inflation there are massive fields that interact with the inflaton field. If these other fields are not much heavier than the Hubble constant during inflation (H) these interactions can lead to important consequences for the cosmological energy density perturbations. The simplest model of this type has a real scalar inflaton field that interacts with another real scalar S (with mass m). In this model there is a mixing term of the form µπS, where π is the Goldstone fluctuation that is associated with the breaking of time translation invariance by the time evolution of the inflaton field during the inflationary era. In this paper we study this model in the region (µ/H) 2 + (m/H) 2 > 9/4 and m/H ∼ O(1) or less. For a large part of the parameter space in this region standard perturbative methods are not applicable. Using numerical and analytic methods we study how large µ/H has to be for the large µ/H effective field theory approach to be applicable.

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 μ. We derive analytic formulas for the curvature perturbation two-, three-, four-, five-, and sixpoint functions explicitly in terms of the external wave vectors in the limit where μ 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 μ=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.

We study a simple extension of quasi-single field inflation in which the inflaton interacts with multiple extra massive scalars known as isocurvatons. Due to the breaking of time translational invariance by the inflaton background, the theory includes kinetic mixings among the inflaton and isocurvatons. These mixings give rise to novel new features in the primordial non-Gaussianities of the scalar curvature perturbation. A noteworthy feature is the amplitude of the squeezed bispectrum can grow nearly as (k s /k l ) −3 while oscillating as cos γ log(k s /k l ), where k s /k l is the ratio of the lengths of the short and long wavevectors. Observation of such a shape would provide evidence for the existence of multiple isocurvatons during inflation. In addition, we consider the effects of these non-Gaussianities on large-scale structure.1 Large non-Gaussianities can also be achieved in more complicated single field models, see for example [6,7].

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