Title: Gaussian Lagrangian Galaxy Bias

Abstract: Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ is usually approximated through a parametric expansion, we show here, that it can also be measured directly from simulations in a non-parameteric way. Our measurements show that the Lagrangian bias function is very close to a Gaussian for halo selections of any mass. Therefore, we newly introduce a Gaussian bias model with several intriguing properties: (1) It predicts only strictly positive probabilities $f > 0$ (unlike expansion models), (2) It has a simple analytic renormalized form and (3) It behaves gracefully in many scenarios where the classical expansion converges poorly. We show that the Gaussian bias model describes the galaxy environment distribution $p(\delta | \mathrm{g})$, the scale dependent bias function $f$ and the renormalized bias function $F$ of haloes and galaxies generally equally well or significantly better than a second order expansion with the same number of parameters. We suggest that a Gaussian bias approach may enhance the range of validity of bias schemes where the canonical expansion converges poorly and further, that it may make new applications possible, since it guarantees the positivity of predicted galaxy densities.