Large-Scale Galaxy Bias (1611.09787v5)

Abstract: This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the clustering of galaxies can be described by a perturbative bias expansion, and the complicated physics of galaxy formation is absorbed by a finite set of coefficients of the expansion, called bias parameters. The review begins with a detailed derivation of this very important result, which forms the basis of the rigorous perturbative description of galaxy clustering, under the assumptions of General Relativity and Gaussian, adiabatic initial conditions. Key components of the bias expansion are all leading local gravitational observables, which include the matter density but also tidal fields and their time derivatives. We hence expand the definition of local bias to encompass all these contributions. This derivation is followed by a presentation of the peak-background split in its general form, which elucidates the physical meaning of the bias parameters, and a detailed description of the connection between bias parameters and galaxy statistics. We then review the excursion-set formalism and peak theory which provide predictions for the values of the bias parameters. In the remainder of the review, we consider the generalizations of galaxy bias required in the presence of various types of cosmological physics that go beyond pressureless matter with adiabatic, Gaussian initial conditions: primordial non-Gaussianity, massive neutrinos, baryon-CDM isocurvature perturbations, dark energy, and modified gravity. Finally, we discuss how the description of galaxy bias in the galaxies' rest frame is related to clustering statistics measured from the observed angular positions and redshifts in actual galaxy catalogs.

• The paper presents a perturbative bias expansion that captures galaxy formation processes using a finite set of bias parameters.
• It applies the peak-background split with a separate universe approach to link long-wavelength density perturbations with local galaxy formation.
• Methodologies including n-point correlations and simulations validate the model, reinforcing its implications for precise cosmological inference.

Overview of "Large-Scale Galaxy Bias"

The paper "Large-Scale Galaxy Bias," authored by Desjacques, Jeong, and Schmidt, provides a comprehensive examination of galaxy bias, which explores the statistical relationship between galaxy distributions and the underlying matter density field. Primarily, this review emphasizes the intricacies of modeling galaxy clustering on large scales, where cosmic density fields exhibit quasi-linear behavior. The research encapsulates the state-of-the-art methodologies in galaxy bias, focusing intensely on the perturbative bias expansion. Here, the intricate physics responsible for galaxy formation is distilled into a finite array of bias parameters within this framework.

Perturbative Bias Expansion

The core of this analysis revolves around deriving a bias expansion that accurately captures the rest-frame density perturbations of galaxies on large scales. This perturbative approach identifies a set of bias parameters that encapsulate the complex formation processes of galaxies into a mathematically tractable model. The bias model proposed accommodates contributions from matter density, tidal fields, and other gravitational observables. These elements are expanded in a local bias framework, robustly anchored in perturbation theory. Stochastic contributions further add to the complexity by accounting for randomness in galaxy formation unrelated to large-scale perturbations.

Peak-Background Split & Response Approach

The authors delve into the peak-background split (PBS), a historical concept that explicates the interplay between long-wavelength density perturbations and local galaxy formation. The PBS perspective is explored with renewed rigor in the context of a separate-universe approach. Here, long-wavelength modes manifest as modifications to the background density in a local universe, offering exact relations for bias parameters. This theoretical proposition aligns with the empirical evaluation of bias parameters via simulations that emulate specific universe conditions.

Measurements and Results

Various methodologies for quantifying the linear and higher-order bias parameters are dissected in the paper. Techniques utilizing n-point correlation functions are the most directly aligned with perturbative expansions outlined, offering clear pathways for measuring linear bias. Simulated results indicate that PBS biases, when measured using structureless simulations, can achieve a high alignment with theoretical predictions for certain formulations of the mass function, notably the Sheth-Tormen variant.

Additionally, moments and scatter plot methods furnish alternative routes to constraining bias parameters but require careful interpretation regarding scale dependence and methodological biases. These are particularly significant when moving from theoretical derivation to practical application in measuring galaxy and halo statistics.

Practical and Theoretical Implications

The implications for cosmology are profound. Understanding galaxy bias is crucial for accurate statistical inference about the universe, particularly when using galaxy clustering to probe cosmological models. The bias parameters directly impact our interpretation of the large-scale structure, facilitating insights into dark matter and dark energy dynamics.

In terms of future applications, this paper sets the stage for refined models accommodating stochastic galaxy formation details and validates scalable frameworks that researchers can employ across different cosmological scenarios, strengthening the linkage between observed galaxy clustering and fundamental cosmological parameters.

Future Directions

The research calls for continuous development in handling stochastic terms and incorporating relativistic effects faithfully on the largest scales. As cosmological surveys increase in scale and precision, the accuracy of galaxy bias becomes ever more critical. The deep connection between theoretical models and observable phenomena highlighted in this analysis makes it a cornerstone of future large-scale structure research, pushing toward a more unified understanding of cosmic evolution.

In conclusion, this paper offers meticulous insights into galaxy bias, expanding the frontier of how we model and interpret large-scale structures. Through its in-depth theoretical frameworks and practical methodologies, it solidifies key concepts in cosmological analysis, providing a crucial toolset for both current research endeavors and future explorations.