Halo bias renormalisation

Abstract

Modern galaxy redshift surveys provide a wealth of information about the evolution of our Universe. They allow to measure both the two-dimensional position on the sky and the distance (given by the cosmological redshift) of millions of galaxies. It is thus possible to obtain a three-dimensional map of the cosmos from which it becomes clear that galaxies are not randomly distributed – instead they build a specific large-scale structure and align in form of a cosmic web. In our current concordance model of cosmology the spatial distribution of luminous objects depends heavily on an underlying, non-visible cosmic web. It consists of dark matter which does not emit electromagnetic radiation and therefore cannot be observed. Its influence on other particles is purely gravitational, and we know that there must be much more dark matter in the Universe than visible matter – otherwise the luminous cosmic web would look completely different from what we observe. Therefore, it is of utmost interest to infer its exact amount and distribution. Theories of gravitational collapse suggest that the formation of dense luminous structures such as galaxies happens in locations where also the dark matter is rather dense. In a two-step process, first the gravitational collapse of dark matter happens, and within the resulting haloes form then the galaxies. The distribution of both haloes and galaxies is therefore biased with respect to the dark matter density field. This leads to the conclusion that we can infer information about dark matter by observing a large number of galaxies. While the overall idea of halo (or galaxy) bias is intuitive to understand, the exact dynamics are still heavily debated. <br /> In this study, we aim to shed light on some of the issues connected to bias. The relation between haloes and dark matter is often phrased in form of a bias expansion up to a certain order that connects various statistical quantities (bias operators) and weighs them with numerical factors (bias parameters). It remains an open question which of these operators are really needed for an accurate description, and what the exact values of the bias parameters are. To address these questions, in chapter 2, we run a suite of 40 cosmological N-body simulations and then compare existing bias models piece by piece to the numerical data. After validating the theoretically motivated shape of individual terms in the data, we fit various complete bias relations against the halo distribution to measure the bias parameters. For that we employ a novel routine that includes the covariance matrix of all terms. Then, using a statistical model selection criterion, we infer the optimal number of bias operators and parameters. We find that for the large halo masses in our simulations a four-parameter model gives the best results. The bias parameters we measure compare excellently with previous results from the literature. <br /> Furthermore, with even greater emphasis, in both chapters 2 and 3 we address a rather technical, but pressing complication that arises in bias models which, so far, has been only examined from a theoretical perspective. When modeling the individual statistical expressions within the framework of cosmological perturbation theory, unphysical extra terms arise at different orders in the expansion. These, while solely due to the mathematical formulation of the problem, distort the measurement of the bias parameters. A correct physical interpretation is therefore made impossible. From theoretical efforts results the approach of bias renormalisation that aims at eliminating these terms order by order in a consistent way. For the first time, we apply this method to numerical data, therefore providing the crucial test of its validity. We are fully successful in renormalising halo bias in simulations at first order (linear bias) as we demonstrate in chapter 2. At second order (quadratic and tidal bias), the issue is more delicate, as we show in chapter 3, where we highlight restrictions on the range of scales for which the method provides satisfying results. <br /> Overall, our findings motivate an application of our model and the renormalisation technique to numerical and also possibly observational data. However, they also clearly expose the limitations of employing perturbative techniques for describing the formation of the large-scale structure of the Universe.