Can we actually constrain $f_{\mathrm{NL}}$ 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 $f_{\mathrm{NL}}$, but the amplitude of the effect is proportional to $f_{\mathrm{NL}}{b}_{\varphi }$, where $b_{\varphi }$ is the linear PNG galaxy bias parameter. Our knowledge of $b_{\varphi }$ is currently very limited, yet nearly all existing $f_{\mathrm{NL}}$ constraints and forecasts assume precise knowledge for it. Here, we use the BOSS DR12 galaxy power spectrum to illustrate how our uncertain knowledge of $b_{\varphi }$ currently prevents us from constraining $f_{\mathrm{NL}}$ with a given statistical precision ${\sigma }_{f_{\mathrm{NL}}}$. Assuming different fixed choices for the relation between $b_{\varphi }$ and the linear density bias $b_1$, we find that ${\sigma }_{f_{\mathrm{NL}}}$ can vary by as much as an order of magnitude. Our strongest bound is $f_{\mathrm{NL}}=16\pm 16(1\sigma )$, while the loosest is $f_{\mathrm{NL}}=230\pm 226(1\sigma )$ for the same BOSS data. The impact of $b_{\varphi }$ can be especially pronounced because it can be close to zero. We also show how marginalizing over $b_{\varphi }$ 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 $f_{\mathrm{NL}}\ne 0$ by constraining the product $f_{\mathrm{NL}}{b}_{\varphi }$, but the error bar ${\sigma }_{f_{\mathrm{NL}}}$ remains undetermined and the results cannot be compared with the CMB; we find $f_{\mathrm{NL}}{b}_{\varphi }\ne 0$ 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 $b_{\varphi }$ parameter, without which we may never be able to competitively constrain $f_{\mathrm{NL}}$ using galaxy data.

15 pages, 6 figures, 3 tables. Comments welcomed! v2 Matches version published in JCAP

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