Prospects for constraining the shape of non-Gaussianity with the scale-dependent bias

We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior of the primordial three-point function in the squeezed limit where one of the momenta is much smaller than the other two. This is potentially interesting since the observation of a three-point function with a squeezed limit that does not go like the local nor equilateral templates would be a signal of non-trivial dynamics during inflation. To this end we use the quasi-single field inflation model of Chen & Wang [1, 2] as a representative two-parameter model, where one parameter governs the amplitude of non-Gaussianity and the other the shape. We also perform a model-independent analysis by parametrizing the scale-dependent bias as a power-law on large scales, where the power is to be constrained from observations. We find that proposed large-scale structure surveys (with characteristics similar to the dark energy task force stage IV surveys) have the potential to distinguish among the squeezed limit behavior of different bispectrum shapes for a wide range of fiducial model parameters. Thus the halo bias can help discriminate between different models of inflation.