Independent constraints on local non-Gaussianity from the peculiar
  velocity and density fields
  Primordial, non-Gaussian perturbations can generate scale-dependent bias in
the galaxy distribution. This in turn will modify correlations between galaxy
positions and peculiar velocities at late times, since peculiar velocities
reflect the underlying matter distribution, whereas galaxies are a biased
tracer of the same. We study this effect, and show that non-Gaussianity can be
constrained by comparing the observed peculiar velocity field to a model
velocity field reconstructed from the galaxy density field assuming linear
bias. The amplitude of the spatial correlations in the residual map obtained
after subtracting one velocity field from the other is directly proportional to
the strength of the primordial non-Gaussianity. We construct the corresponding
likelihood function use it to constrain the amplitude of the linear flow
$\beta$ and the amplitude of local non-Gaussianity $f^{\rm NL}_{\rm local}$.
Applying our method to two observational data sets, the Type-Ia supernovae
(A1SN) and Spiral Field \textit{I}-band (SFI++) catalogues, we obtain
constraints on the linear flow parameter consistent with the values derived
previously assuming Gaussianity. The marginalised 1-D distribution of $|f^{\rm
NL}_{\rm local}|$ does not show strong evidence for non-zero $f^{\rm NL}_{\rm
local}$, and we set 95% upper limits $|f^{\rm NL}_{\rm local}|<51.4$ from A1SN
and $|f^{\rm NL}_{\rm local}|<92.6$ from SFI++. These limits on $f^{\rm
NL}_{\rm local}$ are as tight as any set by previous large-scale structure
measurements. Our method can be applied to any survey with radial velocities
and density field data, and provides an independent check of recent CMB
constraints on $f^{\rm NL}_{\rm local}$, extending these to smaller spatial
scales.
