Use of delta N formalism - Difficulties in generating large local-type non-Gaussianity during inflation -

TL;DR

This paper analyzes the challenges of generating large local-type non-Gaussianity during inflation using the delta N formalism, highlighting the limitations in various inflation models and the conditions needed for observable non-Gaussianity.

Contribution

It provides a general formula for non-linearity during inflation and demonstrates the difficulties in achieving large non-Gaussianity across different inflation scenarios.

Findings

Non-Gaussianity is proportional to slow-roll parameters and model-dependent factors.

Temporal violation of slow roll alone is insufficient for large non-Gaussianity.

Unnatural initial conditions are required in some models to produce observable non-Gaussianity.

Abstract

We discuss generation of non-Gaussianity in density perturbation through the super-horizon evolution during inflation by using the so-called $\delta N$ formalism. We first provide a general formula for the non-linearity parameter generated during inflation. We find that it is proportional to the slow-roll parameters, multiplied by the model dependent factors that may enhance the non-gaussianity to the observable ranges. Then we discuss three typical examples to illustrate how difficult to generate sizable non-Gaussianity through the super-horizon evolution. First example is the double inflation model, which shows that temporal violation of slow roll conditions is not enough for the generation of non-Gaussianity. Second example is the ordinary hybrid inflation model, which illustrates the importance of taking into account perturbations on small scales. Finally, we discuss Kadota-Stewart model. This model gives an example in which we have to choose rather unnatural initial conditions even if large non-Gaussianity can be generated.