The smearing scale in Laguerre reconstructions of the correlation function

Abstract

To a good approximation, on large cosmological scales the evolved two-point correlation function of biased tracers is related to the initial one by a convolution. For Gaussian initial conditions, the smearing kernel is Gaussian, so if the initial correlation function is parametrized using simple polynomials then the evolved correlation function is a sum of generalized Laguerre functions of half-integer order. This motivates an analytic Laguerre reconstruction algorithm which previous work has shown is fast and accurate. This reconstruction requires as input the width of the smearing kernel. We show that the method can be extended to estimate the width of the smearing kernel from the same dataset. This estimate, and associated uncertainties, can then be used to marginalize over the distribution of reconstructed shapes, and hence provide error estimates on the value of the distance scale which are not tied to a particular cosmological model. We also show that if, instead, we parametrize the evolved correlation function using simple polynomials, then the initial one is a sum of Hermite polynomials, again enabling fast and accurate deconvolution. If one is willing to use constraints on the smearing scale from other datasets, then marginalizing over its value is simpler for Hermite reconstruction, potentially providing further speed-up in cosmological analyses.

arXiv comment11 pages, 6 figures

References in corpus (20)

• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• The Galaxy Luminosity Function and Luminosity Density at Redshift z=0.1
• A 2% Distance to z=0.35 by Reconstructing Baryon Acoustic Oscillations - I : Methods and Application to the Sloan Digital Sky Survey
• Galaxy Evolution from Halo Occupation Distribution Modeling of DEEP2 and SDSS Galaxy Clustering
• Nonlinear Evolution of Baryon Acoustic Oscillations
• The Quijote simulations
• Combining Full-Shape and BAO Analyses of Galaxy Power Spectra: A 1.6% CMB-independent constraint on H0
• `Eppur Si Muove': On The Motion of the Acoustic Peak in the Correlation Function
• Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Redshift space correlations and scale-dependent stochastic biasing of density peaks
• Iterative initial condition reconstruction
• The Evolution of Correlation Functions in the Zel'dovich Approximation and its Implications for the Validity of Perturbation Theory
• Cosmic distance inference from purely geometric BAO methods: Linear Point standard ruler and Correlation Function Model Fitting
• The Impact of Wrong Assumptions in BAO Reconstruction
• Beating non-linearities: improving the Baryon Acoustic Oscillations with the linear point
• BAO reconstruction: a swift numerical action method for massive spectroscopic surveys
• The effects of massive neutrinos on the linear point of the correlation function
• The Sinc Function Representation and Three-Loop Master Diagrams
• Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues

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