Scale dependence of $f_{NL}$ in N-flation

TL;DR

This paper derives the spectral index of $f_{NL}$ in N-flation models, showing that axion N-flation with varying decay constants can produce a detectable tilt, which can help distinguish it observationally.

Contribution

It provides a general derivation of the spectral index of $f_{NL}$ in N-flation and analyzes its behavior in axion N-flation models with different decay constants.

Findings

$n_{f_{NL}}$ is negligible when inflatons have identical potentials.

A negative, detectable $n_{f_{NL}}$ can occur in axion N-flation with varying decay constants.

Measurement of $n_{f_{NL}}$ can test the validity of axion N-flation models.

Abstract

Adopting the horizon-crossing approximation, we derive the spectral index of $f_{NL}$ in general N-flation model. Axion N-flation model is taken as a typical model for generating a large $f_{NL}$ which characterizes the size of local form bispectrum. We find that its tilt $n_{f_{NL}}$ is negligibly small when all inflatons have the same potential, but a negative detectable $n_{f_{NL}}$ can be achieved in the axion N-flation with different decay constants for different inflatons. The measurement of $n_{f_{NL}}$ can be used to support or falsify the axion N-flation in the near future.