Modeling Biased Tracers at the Field Level

In this talk I will show how well the perturbative halo bias model works at the field level. The advantage of this approach is that all measurements can be done without sample variance if the same initial conditions are used in simulations and perturbation theory calculations. For this purpose, modified bias operators in Eulerian space are defined, 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. 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. 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 reconstructions that require precise estimates of the large-scale potential from the biased tracer density.