Constraints on local primordial non-Gaussianity from large scale structure

Recent work has shown that the local non-Gaussianity parameter fNL induces a scale dependent bias, whose amplitude is growing with scale. Here we first rederive this result within the context of the peak–background split formalism and show that it only depends on the assumption of universality of the mass function, assuming that the halo bias only depends on the mass. We then use the extended Press–Schechter formalism to argue that this assumption may be violated and that the scale dependent bias will depend on other properties, such as the merging history of halos. In particular, in the limit of recent mergers we find that the effect is suppressed. Next we use these predictions in conjunction with a compendium of large scale data to put a limit on the value of fNL. When combining all data assuming that the halo occupation depends only on the halo mass, we get a limit of -29 (-65)<fNL<+70 (+93) at 95% (99.7%) confidence. While we use a wide range of data sets, our combined result is dominated by the signal from the SDSS photometric quasar sample. If the latter are modeled as recent mergers then the limits weaken to -31 (-96)<fNL<+70 (+96). These limits are comparable to the strongest current limits from the Wilkinson Anisotropy Probe (WMAP) five-year analysis, with no evidence of a positive signal in fNL. While the method needs to be thoroughly tested against large scale structure simulations with realistic quasar and galaxy formation models, our results indicate that this is a competitive method relative to the cosmic microwave background one and should be further pursued both observationally and theoretically.