Constraining primordial and gravitational mode coupling with the
  position-dependent bispectrum of the large-scale structure
  We develop and study the position-dependent bispectrum. It is a
generalization of the recently proposed position-dependent power spectrum
method of measuring the squeezed-limit bispectrum. The position-dependent
bispectrum can similarly be used to measure the squeezed-limit trispectrum in
which one of the wavelengths is much longer than the other three. In this work,
we will mainly consider the case in which the three smaller wavelengths are
nearly the same (the equilateral configuration). We use the Fisher information
matrix to forecast constraints on bias parameters and the amplitude of
primordial trispectra from the position-dependent bispectrum method. We find
that the method can constrain the local-type $g_{\rm NL}$ at a level of
$\sigma(g_{\rm NL}^{\rm local}) \approx 3 \times 10^5$ for a large volume
SPHEREx-like survey; improvements can be expected by including all the
triangular configurations of the bispectra rather than just the equilateral
configuration. However, the same measurement would also constrain a much larger
family of trispectra than local $g_{\rm NL}$ model. We discuss the implications
of the forecasted reach of future surveys in terms of super cosmic variance
uncertainties from primordial non-Gaussianities.
