  Quasi-single field inflation predicts a peculiar momentum dependence in the
squeezed limit of the primordial bispectrum which smoothly interpolates between
the local and equilateral models. This dependence is directly related to the
mass of the isocurvatons in the theory which is determined by the
supersymmetry. Therefore, in the event of detection of a non-zero primordial
bispectrum, additional constraints on the parameter controlling the
momentum-dependence in the squeezed limit becomes an important question. We
explore the effects of these non-Gaussian initial conditions on large-scale
structure and the cosmic microwave background, with particular attention to the
galaxy power spectrum at large scales and scale-dependence corrections to
galaxy bias. We determine the simultaneous constraints on the two parameters
describing the QSF bispectrum that we can expect from upcoming large-scale
structure and cosmic microwave background observations. We find that for
relatively large values of the non-Gaussian amplitude parameters, but still
well within current uncertainties, galaxy power spectrum measurements will be
able to distinguish the QSF scenario from the predictions of the local model. A
CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is
also a range of parameter values for which Planck data may be able distinguish
between QSF models and the related local and equilateral shapes. Given the
different observational weightings of the CMB and LSS results, degeneracies can
be significantly reduced in a joint analysis.
