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 bϕ , where bϕ is the linear PNG galaxy bias parameter. Our knowledge of bϕ 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 bϕ currently prevents us from constraining f NL with a given statistical precision σ fNL. Assuming different fixed choices for the relation between bϕ and the linear density bias b 1, we find that σ fNL can vary by as much as an order of magnitude. Our strongest bound is f NL = 16 ± 16 (1σ), while the loosest is f NL = 230 ± 226 (1σ) for the same BOSS data. The impact of bϕ can be especially pronounced because it can be close to zero. We also show how marginalizing over bϕ 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 bϕ , but the error bar σ fNL remains undetermined and the results cannot be compared with the CMB; we find f NL bϕ ≠ 0 with 1.6σ 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 bϕ parameter, without which we may never be able to competitively constrain f NL using galaxy data.