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

Single-field slow-roll inflation with a nonvacuum initial state has an enhanced bispectrum in the local limit. We numerically calculate the local-type f(NL) signal in the cosmic microwave background (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) approximate to eta(0)k (justified by physical reasons discussed within) and epsilon less than or similar to 0.01, we find that 0 < f(NL) < 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), f(NL) can be much larger and/or negative (depending on the choice of theta(k)), e. g. f(NL) approximate to 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 f(NL) that is considerably larger than that usually predicted from single-field inflation.