Non-Gaussian Shape Discrimination with Spectroscopic Galaxy Surveys
  [Abridged] We consider how galaxy clustering data, from Mpc to Gpc scales,
from upcoming large scale structure surveys, such as Euclid and DESI, can
provide discriminating information about the bispectrum shape arising from a
variety of inflationary scenarios. Through exploring in detail the weighting of
shape properties in the calculation of the halo bias and halo mass function we
show how they probe a broad range of configurations, beyond those in the
squeezed limit, that can help distinguish between shapes with similar large
scale bias behaviors.
  We assess the impact, on constraints for a diverse set of non-Gaussian
shapes, of galaxy clustering information in the mildly non-linear regime, and
surveys that span multiple redshifts and employ different galactic tracers of
the dark matter distribution. Fisher forecasts are presented for a Euclid-like
spectroscopic survey of H$\alpha$-selected emission line galaxies (ELGs) using
recent revisions of the expected H$\alpha$ luminosity function, and a DESI-like
survey, of luminous red galaxies (LRGs) and [O-II] doublet-selected ELGs, in
combination with Planck-like CMB temperature and polarization data.
  While ELG samples provide better probes of shapes that are divergent in the
squeezed limit, LRG constraints, centered below $z<1$, yield stronger
constraints on shapes with scale-independent large-scale halo biases, such as
the equilateral template. The ELG and LRG samples provide complementary
degeneracy directions for distinguishing between different shapes. If the
Gaussian galaxy bias is constrained to better than a percent level, such as can
be determined from the galaxy bispectrum or weak lensing, then the LSS and CMB
data could provide complementary constraints that will enable differentiation
of bispectra with distinct theoretical origins but with similar large scale,
squeezed-limit properties.
