The Evolution of Correlation Functions in the Zel'dovich Approximation and its Implications for the Validity of Perturbation Theory

Abstract

We investigate whether it is possible to study perturbatively the transition in cosmological clustering between a single streamed flow to a multi streamed flow. We do this by considereing a system whose dynamics is governed by the Zel'dovich approximation (ZA) and calculating the evolution of the two point correlation function using two methods: 1.Distribution functions 2.Hydrodynamic equations without pressure and vorticity. The latter method breaks down once multistreaming occurs whereas the former does not. We find that the two methods give the same results to all orders in a perturbative expansion of the two point correlation function. We thus conclude that we cannot study the transition from a single stream flow to a multi-stream flow in a perturbative expansion. We expect this conclusion to hold even if we use the full gravitational dynamics (GD) instead of ZA. We use ZA to look at the evolution of the two point correlation function at large spatial separations and we find that until the onset of multi-streaming the evolution can be described by a diffusion process where the linear evolution at large scales gets modified by the rearrangement of matter on small scales. We compare these results with the lowest order nonlinear results from GD. We find that the difference is only in the numerical value of the diffusion coefficient and we interpret this physically. We also use ZA to study the induced three point correlation function. At the lowest order we find that, as in the case of GD, the three point correlation does not necessarily have the hierarchical form. We also find that at large separations the effect of the higher order terms for the three point correlatin function is very similar to that for the the two point correlation and in this case too the evolution can be be described in terms of

28 pages including 6 figures, Latex, Aastex macros, Accepted in Astrophysical Journal

Cited by in corpus (49)

• SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
• Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample
• Large-Scale Galaxy Bias
• Nonlinear Evolution of Baryon Acoustic Oscillations
• Interpreting large-scale redshift-space distortion measurements
• Towards an accurate model of the redshift space clustering of halos in the quasilinear regime
• Convolution Lagrangian perturbation theory for biased tracers
• A critical look at cosmological perturbation theory techniques
• A new analysis of galaxy 2-point functions in the BOSS survey, including full-shape information and post-reconstruction BAO
• A Lagrangian effective field theory
• `Eppur Si Muove': On The Motion of the Acoustic Peak in the Correlation Function
• Non-linear structure formation and the acoustic scale
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• Redshift-Space Distortions in Lagrangian Perturbation Theory
• Calibrating the Baryon Oscillation Ruler for Matter and Halos
• Reconstructing baryon oscillations
• Fractal Dimension as a measure of the scale of Homogeneity
• Cosmological Perturbations: Entering the Non-Linear Regime
• A marked correlation function for constraining modified gravity models
• Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys
• Tracing The Sound Horizon Scale With Photometric Redshift Surveys
• Adhesive Gravitational Clustering
• Exploring redshift-space distortions in large-scale structure
• Statistics of the epoch of reionization (EoR) 21-cm signal -- II. The evolution of the power spectrum error-covariance
• Testing Gravity Using Large-Scale Redshift-Space Distortions
• Particle mesh simulations of the Lyman-alpha forest and the signature of Baryon Acoustic Oscillations in the intergalactic medium
• Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results
• Non-linear evolution of the BAO scale in alternative theories of gravity
• A non-singular bouncing cosmology in $f(R,T)$ gravity
• Dynamics of gravitational clustering I. Building perturbative expansions
• The Impact of Wrong Assumptions in BAO Reconstruction
• Beating non-linearities: improving the Baryon Acoustic Oscillations with the linear point
• Dynamics of gravitational clustering V. Subleading corrections in the quasi-linear regime
• Evolution of the Pairwise Peculiar Velocity Distribution Function in Lagrangian Perturbation Theory
• Optimal Transport Reconstruction of Baryon Acoustic Oscillations
• Impacts of biasing schemes in the one-loop integrated perturbation theory
• The dark matter dispersion tensor in perturbation theory
• Volume Statistics as a Probe of Large-Scale Structure
• Nonlinear redshift distortions: The two-point correlation function
• Phenomenology of BAO evolution from Lagrangian to Eulerian Space
• The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter
• Self-similarity and the Pair Velocity Dispersion
• Cosmology at high redshift -- a probe of fundamental physics
• The smearing scale in Laguerre reconstructions of the correlation function
• Analytical Equation of Three-point Correlation Function of Galaxies: to Third Order of Density Perturbation
• On the origin of transient features in cosmological N-Body Simulations
• Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues
• Web-Halo Model (WHM): Accurate non-linear matter power spectrum predictions without free parameters
• Laguerre reconstruction of the correlation function on Baryon Acoustic Oscillation scales