Primordial non-Gaussianity: Large-scale structure signature in the perturbative bias model

I compute the effect on the power spectrum of tracers of the large-scale mass-density field (e.g., galaxies) of primordial non-Gaussianity of the form Φ=φ+fNL(φ2-<φ2>)+gNLφ3+..., where Φ is proportional to the initial potential fluctuations and φ is a Gaussian field, using beyond-linear-order perturbation theory. I find that the need to eliminate large higher-order corrections necessitates the addition of a new term to the bias model, proportional to φ, i.e., δg=bδδ+bφfNLφ+..., with all the consequences this implies for clustering statistics, e.g., Pgg(k)=bδ2Pδδ(k)+2bδbφfNLPφδ(k)+bφ2fNL2Pφφ(k)+.... This result is consistent with calculations based on a model for dark matter halo clustering, showing that the form is quite general, not requiring assumptions about peaks, or the formation or existence of halos. The halo model plays the same role it does in the usual bias picture, giving a prediction for bφ for galaxies known to sit in a certain type of halo. Previous projections for future constraints based on this effect have been very conservative--there is enough volume at z < or approx. 2 to measure fNL to ∼±1, with much more volume at higher z. As a prelude to the bias calculation, I point out that the beyond-linear (in φ) corrections to the power spectrum of mass-density perturbations are naively infinite, so it is dangerous to assume they are negligible; however, the infinite part can be removed by a renormalization of the fluctuation amplitude, with the residual k-dependent corrections negligible for models allowed by current constraints.