Abstract
In this work, we extend the idea of Quasi Single Field inflation [1] to the case of multiple isocurvaton fields with masses of order of Hubble, which are coupled kinetically to the inflaton field and have some interactions among themselves. We consider the effects of these massive modes in both the size and the shape of the bispectrum. We show that the shape of the bispectrum in the squeezed limit is dominated by the lightest field and is the same as in Quasi Single Field inflation. This is a generic feature of multiple isocurvaton fields and is independent of the details of the interactions among the massive fields. When the isocurvaton fields have similar masses, we can potentially distinguish two different shapes in the squeezed limit so that the shape of the bispectrum can act as a particle detector. However, in the presence of hierarchy among the massive fields, the dominant effect is due to the lightest field.
Highlights
Inflation is the leading paradigm for early universe and structure formation which is well consistent with recent observations from Planck satellite [2, 3]
We study the perturbation at the quadratic level, considering the free field action as well as the exchange vertex interactions which are necessary in order to convert the contribution from the isocurvaton fields into the curvature perturbation
We look at the term with the permutation k1 ↔ k3
Summary
The equations of motion for σi0(t), (i = 0, 1) and θ0(t) are σi0 = const In this picture σi’s have been stabilized around their background values while the inflaton field θ is slowly rolling along the potential Vsr. we can specify the form of the V (σ1, σ1) up to the third orders in fields perturbations which will be used to calculate the bispectrum δV (σ1, σ2). The solution for the inflaton mode function, uk, imposing the Minkowski initial condition for modes deep inside the horizon is uk = H (1 + ikτ )e−ikτ As it has been mentioned in [1], there are three different regions in the mass parameter space of σi’s, in which vk and wk can be either over-damped corresponding to
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