The clustering of galaxies and galaxy clusters: constraints on
  primordial non-Gaussianity from future wide-field surveys
  We investigate the constraints on primordial non-Gaussianity with varied
bispectrum shapes that can be derived from the power spectrum of galaxies and
clusters of galaxies detected in future wide field optical/near-infrared
surveys. Having in mind the proposed ESA space mission \emph{Euclid} as a
specific example, we combine the spatial distribution of spectroscopically
selected galaxies with that of weak lensing selected clusters. We use the
physically motivated halo model in order to represent the correlation function
of arbitrary tracers of the Large Scale Structure in the Universe. As naively
expected, we find that galaxies are much more effective in jointly constrain
the level of primordial non-Gaussianity $f_\mathrm{NL}$ and the amplitude of
the matter power spectrum $\sigma_8$ than clusters of galaxies, due to the much
lower abundance of the latter that is not adequately compensated by the larger
effect on the power spectrum. Nevertheless, combination of the galaxy power
spectrum with the cluster-galaxy cross spectrum can decrease the error on the
determination of $f_\mathrm{NL}$ by up to a factor of $\sim 2$. This decrement
is particularly evident for the less studied non-Gaussian bispectrum shapes,
the so-called enfolded and the orthogonal ones. Setting constraints on these
models can shed new light on various aspects of the physics of the early
Universe, and it is hence of extreme importance. By combining the power spectra
of clusters and galaxies with the cluster-galaxy cross spectrum we find
constraints on primordial non-Gaussianity of the order $\Delta f_\mathrm{NL}
\sim $ a few, competitive and possibly superior to future CMB experiments.
