Peaks theory and the excursion set approach

Abstract

We describe a model of dark matter halo abundances and clustering which combines the two most widely used approaches to this problem: that based on peaks and the other based on excursion sets. Our approach can be thought of as addressing the cloud-in-cloud problem for peaks and/or modifying the excursion set approach so that it averages over a special subset, rather than all possible walks. In this respect, it seeks to account for correlations between steps in the walk as well as correlations between walks. We first show how the excursion set and peaks models can be written in the same formalism, and then use this correspondence to write our combined excursion set peaks model. We then give simple expressions for the mass function and bias, showing that even the linear halo bias factor is predicted to be k-dependent as a consequence of the nonlocality associated with the peak constraint. At large masses, our model has little or no need to rescale the variable delta_c from the value associated with spherical collapse, and suggests a simple explanation for why the linear halo bias factor appears to lie above that based on the peak-background split at high masses when such a rescaling is assumed. Although we have concentrated on peaks, our analysis is more generally applicable to other traditionally single-scale analyses of large-scale structure.

10 pages, 4 figures; v2 -- minor changes, added discussion in sec2.2, fixed a typo. Accepted in MNRAS

References in corpus (3)

• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• Dark matter halo creation in moving barrier models

Cited by in corpus (79)

• Large-Scale Galaxy Bias
• Precision measurement of the local bias of dark matter halos
• Non-linear statistics of primordial black holes from gaussian curvature perturbations
• Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses
• Non-local Lagrangian bias
• From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)
• Some like it triaxial: the universality of dark matter halo shapes and their evolution along the cosmic time
• Large-Scale Clustering of Cosmic Voids
• Excursion set peaks: a self-consistent model of dark halo abundances and clustering
• Bias Loop Corrections to the Galaxy Bispectrum
• Testing one-loop galaxy bias: joint analysis of power spectrum and bispectrum
• Verifying the consistency relation for the scale-dependent bias from local primordial non-Gaussianity
• Large-scale assembly bias of dark matter halos
• The nature of voids: I. Watershed void finders and their connection with theoretical models
• Machine learning cosmological structure formation
• Sloan Digital Sky Survey III Photometric Quasar Clustering: Probing the Initial Conditions of the Universe using the Largest Volume
• The multidimensional dependence of halo bias in the eye of a machine: a tale of halo structure, assembly and environment
• Cluster-Void Degeneracy Breaking: Dark Energy, Planck and the Largest Cluster & Void
• Primordial black holes from metric preheating: mass fraction in the excursion-set approach
• Voids in Modified Gravity Reloaded: Eulerian Void Assignment
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Non-local halo bias with and without massive neutrinos
• Bias deconstructed: Unravelling the scale dependence of halo bias using real space measurements
• A local bias approach to the clustering of discrete density peaks
• Testing spherical evolution for modelling void abundances
• Lagrangian bias of generic large-scale structure tracers
• An improved model of HII bubbles during the epoch of reionization
• The importance of stepping up in the excursion set approach
• Self-consistency of the Excursion Set Approach
• Measuring nonlocal Lagrangian peak bias
• The locations of halo formation and the peaks formalism
• Weighing neutrinos with the halo environment
• When do cosmic peaks, filaments or walls merge? A theory of critical events in a multi-scale landscape
• The universal multiplicity function: counting halos and voids
• Taming assembly bias for primordial non-Gaussianity
• The excursion set approach in non-Gaussian random fields
• Stochastic bias in multi-dimensional excursion set approaches
• Effective Window Function for Lagrangian Halos
• Fixing a Rigorous Formalism for the Accurate Analytic Derivation of Halo Properties
• Impacts of biasing schemes in the one-loop integrated perturbation theory
• Non-Gaussian bias: insights from discrete density peaks
• On the Markovian assumption in the excursion set approach: the approximation of Markov Velocities
• Halo Mass Definition and Multiplicity Function
• Phenomenology of BAO evolution from Lagrangian to Eulerian Space
• Excursion set peaks in energy as a model for haloes
• Constraints on halo formation from cross-correlations with correlated variables
• Culminating the peak CUSP to descry the dark side of halos
• Isotropic extragalactic flux from dark matter annihilations: lessons from interacting dark matter scenarios
• The bias of weighted dark matter halos from peak theory
• Excursion Set Theory for Correlated Random Walks
• Cosmology with Galaxy Clusters: Systematic Effects in the Halo Mass Function
• Statistics of Dark Matter Halos in the Excursion Set Peak Framework
• Non-perturbative halo clustering from cosmological density peaks
• Dark matter halo mass functions and density profiles from mass and energy cascade
• Choose to smooth: Gaussian streaming with the truncated Zel'dovich approximation
• Cosmological Filaments in the light of Excursion Set of Saddle Points
• On the projected mass distribution around galaxy clusters : a Lagrangian theory of harmonic power spectra
• Consistency relations for the Lagrangian halo bias and their implications
• Halo mass function in scale invariant models
• Getting in shape with minimal energy. A variational principle for protohaloes
• A Stochastic Theory of the Hierarchical Clustering II. Halo progenitor mass function and large-scale bias
• Modelling the 21 cm Signal From the Epoch of Reionization and Cosmic Dawn
• Tidal shear and the consistency of microscopic Lagrangian halo approaches
• Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier
• Velocity bias and the nonlinear perturbation theory of peaks
• The large-separation expansion of peak clustering in Gaussian random fields
• Probing the Epoch of Reionization using synergies of line intensity mapping
• Voids and Halos in Voids statistics as a probe of the Expansion History of the Universe
• Stochasticity in halo formation and the excursion set approach
• Accurate halo mass functions from the simplest excursion set theory
• Mass accretion rates and multi-scale halo environment in cold and warm dark matter cosmologies
• Mass assembly history of dark matter halos in the light of $H_0$ tension
• A Stochastic Theory of the Hierarchical Clustering III. The Non-universality and Non-stationarity of the Halo Mass Function
• MUSE-DARK III: The evolution of the radial acceleration relation at intermediate redshifts
• Approximate methods for the generation of dark matter halo catalogs in the age of precision cosmology
• Probabilistic Lagrangian bias estimators and the cumulant bias expansion
• The Extended Zel'dovich Mass Functions of Clusters and Isolated Clusters in the Presence of Primordial Non-Gaussianity
• Prompt cusps in hierarchical dark matter halos: Implications for annihilation boost
• Segmenting proto-halos with vision transformers