The squeezed limit of the bispectrum in multi-field inflation

We calculate the squeezed limit of the bispectrum produced by inflation with multiple light fields. To achieve this we allow for different horizon exit times for each mode and calculate the intrinsic field-space three-point function in the squeezed limit using soft-limit techniques. We then use the $\delta N$ formalism from the time the last mode exits the horizon to calculate the bispectrum of the primordial curvature perturbation. We apply our results to calculate the spectral index of the halo bias, $n_{\delta b}$, an important observational probe of the squeezed limit of the primordial bispectrum and compare our results with previous formulae. We give an example of a curvaton model with $n_{\delta b} \sim {\cal O}(n_s-1)$ for which we find a 20% correction to observable parameters for squeezings relevant to future experiments. For completeness, we also calculate the squeezed limit of three-point correlation functions involving gravitons for multiple field models.