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. (arXiv:2205.05673v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Barreira_A/0/1/0/all/0/1">Alexandre Barreira</a>
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. Our
strongest bound is $f_{rm NL} = 16 pm 16 (1sigma)$, while the loosest is
$f_{rm NL} = 230 pm 226 (1sigma)$ 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 $f_{rm NL} neq 0$ by
constraining the product $f_{rm NL}b_{phi}$, but the error bar
$sigma_{f_{rm NL}}$ remains undetermined and the results cannot be compared
with the CMB; we find $f_{rm NL}b_{phi} neq 0$ with $1.6sigma$
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
$f_{rm NL}$ using galaxy data.
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. Our
strongest bound is $f_{rm NL} = 16 pm 16 (1sigma)$, while the loosest is
$f_{rm NL} = 230 pm 226 (1sigma)$ 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 $f_{rm NL} neq 0$ by
constraining the product $f_{rm NL}b_{phi}$, but the error bar
$sigma_{f_{rm NL}}$ remains undetermined and the results cannot be compared
with the CMB; we find $f_{rm NL}b_{phi} neq 0$ with $1.6sigma$
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
$f_{rm NL}$ using galaxy data.
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