Modeling Biased Tracers at the Field Level. (arXiv:1811.10640v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Schmittfull_M/0/1/0/all/0/1">Marcel Schmittfull</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Simonovic_M/0/1/0/all/0/1">Marko Simonović</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Assassi_V/0/1/0/all/0/1">Valentin Assassi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zaldarriaga_M/0/1/0/all/0/1">Matias Zaldarriaga</a>
In this paper we test the perturbative halo bias model at the field level.
The advantage of this approach is that any analysis can be done without sample
variance if the same initial conditions are used in simulations and
perturbation theory calculations. We write the bias expansion in terms of
modified bias operators in Eulerian space, designed such that the large bulk
flows are automatically resummed and not treated perturbatively. Using these
operators, the bias model accurately matches the Eulerian density of halos in
N-body simulations. The mean-square model error is close to the Poisson shot
noise for a wide range of halo masses and it is rather scale-independent, with
scale-dependent corrections becoming relevant at the nonlinear scale. In
contrast, for linear bias the mean-square model error can be higher than the
Poisson prediction by factors of up to a few on large scales, and it becomes
scale dependent already in the linear regime. We show that by weighting
simulated halos by their mass, the mean-square error of the model can be
further reduced by up to an order of magnitude, or by a factor of two when
including $0.2$ dex mass scatter. We also test the Standard Eulerian bias model
using the nonlinear matter field measured from simulations and show that it
leads to a larger and more scale-dependent model error than the bias expansion
based on perturbation theory. These results may be of particular relevance for
cosmological inference methods that use a likelihood of the biased tracer at
the field level, or for initial condition and BAO reconstruction that requires
a precise estimate of the large-scale potential from the biased tracer density.
In this paper we test the perturbative halo bias model at the field level.
The advantage of this approach is that any analysis can be done without sample
variance if the same initial conditions are used in simulations and
perturbation theory calculations. We write the bias expansion in terms of
modified bias operators in Eulerian space, designed such that the large bulk
flows are automatically resummed and not treated perturbatively. Using these
operators, the bias model accurately matches the Eulerian density of halos in
N-body simulations. The mean-square model error is close to the Poisson shot
noise for a wide range of halo masses and it is rather scale-independent, with
scale-dependent corrections becoming relevant at the nonlinear scale. In
contrast, for linear bias the mean-square model error can be higher than the
Poisson prediction by factors of up to a few on large scales, and it becomes
scale dependent already in the linear regime. We show that by weighting
simulated halos by their mass, the mean-square error of the model can be
further reduced by up to an order of magnitude, or by a factor of two when
including $0.2$ dex mass scatter. We also test the Standard Eulerian bias model
using the nonlinear matter field measured from simulations and show that it
leads to a larger and more scale-dependent model error than the bias expansion
based on perturbation theory. These results may be of particular relevance for
cosmological inference methods that use a likelihood of the biased tracer at
the field level, or for initial condition and BAO reconstruction that requires
a precise estimate of the large-scale potential from the biased tracer density.
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