Can we actually constrain fNL using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum

Abstract The scale-dependent bias effect on the galaxy power spectrum is a very promising probe of the local primordial non-Gaussianity (PNG) parameter f NL , but the amplitude of the effect is proportional to f NL b ϕ , where b ϕ is the linear PNG galaxy bias parameter. Our knowledge of b ϕ is currently very limited, yet nearly all existing f NL constraints and forecasts assume precise knowledge for it. Here, we use the BOSS DR12 galaxy power spectrum to illustrate how our uncertain knowledge of b ϕ currently prevents us from constraining f NL with a given statistical precision σ f NL . Assuming different fixed choices for the relation between b ϕ and the linear density bias b 1 , we find that σ f NL can vary by as much as an order of magnitude. Our strongest bound is f NL = 16 ± 16 (1 σ ), while the loosest is f NL = 230 ± 226 (1 σ ) for the same BOSS data. The impact of b ϕ can be especially pronounced because it can be close to zero. We also show how marginalizing over b ϕ with wide priors is not conservative, and leads in fact to biased constraints through parameter space projection effects. Independently of galaxy bias assumptions, the scale-dependent bias effect can only be used to detect f NL ≠ 0 by constraining the product f NL b ϕ , but the error bar σ f NL remains undetermined and the results cannot be compared with the CMB; we find f NL b ϕ ≠ 0 with 1.6 σ significance. We also comment on why these issues are important for analyses with the galaxy bispectrum. Our results strongly motivate simulation-based research programs aimed at robust theoretical priors for the b ϕ parameter, without which we may never be able to competitively constrain f NL using galaxy data.