Calculating the local-type fNL for slow-roll inflation with a non-vacuum initial state

TL;DR

This paper numerically calculates the local-type fNL parameter in slow-roll inflation with a non-vacuum initial state, showing potential for detectable non-Gaussianity depending on model parameters, which exceeds typical single-field predictions.

Contribution

It provides the first detailed numerical computation of the local fNL in non-vacuum initial states for slow-roll inflation, including full transfer effects and parameter dependencies.

Findings

fNL ranges from 0 to 1.52 in conservative cases.

Allowing certain parameters, fNL can be as large as 28 or -6.4.

Some scenarios could be detectable by Planck or future satellites.

Abstract

Single-field slow-roll inflation with a non-vacuum initial state has an enhanced bispectrum in the local limit. We numerically calculate the local-type fNL signal in the CMB that would be measured for such models (including the full transfer function and 2D projection). The nature of the result depends on several parameters, including the occupation number N_k, the phase angle \theta_k between the Bogoliubov parameters, and the slow-roll parameter \epsilon. In the most conservative case, where one takes \theta_k \approx \eta_0 k (justified by physical reasons discussed within) and \epsilon\lesssim 0.01, we find that 0 < fNL < 1.52 (\epsilon/0.01), which is likely too small to be detected in the CMB. However, if one is willing to allow a constant value for the phase angle \theta_k and N_k=O(1), fNL can be much larger and/or negative (depending on the choice of \theta_k), e.g. fNL \approx 28 (\epsilon/0.01) or -6.4 (\epsilon/0.01); depending on \epsilon, these scenarios could be detected by Planck or a future satellite. While we show that these results are not actually a violation of the single-field consistency relation, they do produce a value for fNL that is considerably larger than that usually predicted from single-field inflation.