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

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

Automated summary

The scale-dependent bias effect is a promising way to study the primordial non-Gaussianity parameter f(NL), but our limited knowledge of the linear PNG galaxy bias parameter b(phi) currently prevents us from accurately constraining f(NL).