Can we actually constrain f_NL 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 local primordial non-Gaussianity (PNG) parameter $f_{\rm NL}$, but amplitude proportional to NL}b_{\phi}$, where $b_{\phi}$ linear PNG parameter. Our knowledge currently limited, yet nearly all existing NL}$ constraints and forecasts assume precise for it. Here, we use BOSS DR12 illustrate how our uncertain prevents us from constraining with given statistical precision $\sigma_{f_{\rm NL}}$. Assuming different fixed choices relation between density $b_1$, find that NL}}$ can vary by as much an order magnitude. strongest bound NL} = 16 \pm 16\ (1\sigma)$, while loosest 230 226\ (1\sigma)$ same data. impact be especially pronounced because it close zero. We also show marginalizing over wide priors not conservative, leads in fact biased through space projection effects. Independently assumptions, only used detect \neq 0$ product error bar remains undetermined results cannot compared CMB; NL}b_{\phi} $1.6\sigma$ significance. comment why these issues are important analyses bispectrum. strongly motivate simulation-based research programs aimed at robust theoretical parameter, without which may never able competitively constrain using