Probing primordial non-Gaussianity with large-scale structure

We consider primordial non-Gaussianity due to quadratic corrections in the gravitational potential parametrized by a nonlinear coupling parameter $f_{\mathrm{NL}}.$ We study constraints on $f_{\mathrm{NL}}$ from measurements of the galaxy bispectrum in redshift surveys. Using estimates for idealized survey geometries of the 2dF and SDSS surveys and realistic ones from SDSS mock catalogs, we show that it is possible to probe $|f_{\mathrm{NL}}|\simeq 100,$ after marginalization over bias parameters. We apply our methods to the galaxy bispectrum measured from the PSCz survey, and obtain a $2\sigma$ constraint $|f_{\mathrm{NL}}|\lesssim 1800.$ We estimate that an all sky redshift survey up to $z\simeq 1$ can probe $|f_{\mathrm{NL}}|\simeq 1.$ We also consider the use of cluster abundance to constrain $f_{\mathrm{NL}}$ and find that in order to be sensitive to $|f_{\mathrm{NL}}|\simeq 100,$ cluster masses need to be determined with an accuracy of a few percent, assuming perfect knowledge of the mass function and cosmological parameters.