Can we actually constrain $f_{\rm NL}$ using the scale-dependent bias effect? An illustration of the impact of galaxy bias uncertainties using the BOSS DR12 galaxy power spectrum

Understand

The scale-dependent bias effect on the galaxy power spectrum is a very promising probe of the local primordial non-Gaussianity (PNG) parameter $f_{\rm NL}$, but the amplitude of the effect is proportional to $f_{\rm NL}b_{\phi}$, where $b_{\phi}$ is the linear PNG galaxy bias parameter.

• Our knowledge of $b_{\phi}$ is currently very limited, yet nearly all existing $f_{\rm NL}$ 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 $f_{\rm NL}$ with a given statistical precision $\sigma_{f_{\rm NL}}$.
• Assuming different fixed choices for the relation between $b_{\phi}$ and the linear density bias $b_1$, we find that $\sigma_{f_{\rm NL}}$ can vary by as much as an order of magnitude.