Cross-correlating 2D and 3D galaxy surveys

Abstract

Galaxy surveys probe both structure formation and the expansion rate, making them promising avenues for understanding the dark universe. Photometric surveys accurately map the 2D distribution of galaxy positions and shapes in a given redshift range, while spectroscopic surveys provide sparser 3D maps of the galaxy distribution. We present a way to analyse overlapping 2D and 3D maps jointly and without loss of information. We represent 3D maps using spherical Fourier-Bessel (sFB) modes, which preserve radial coverage while accounting for the spherical sky geometry, and we decompose 2D maps in a spherical harmonic basis. In these bases, a simple expression exists for the cross-correlation of the two fields. One very powerful application is the ability to simultaneously constrain the redshift distribution of the photometric sample, the sample biases, and cosmological parameters. We use our framework to show that combined analysis of DESI and LSST can improve cosmological constraints by factors of $\sim 1.2$ to $\sim 1.8$ on the region where they overlap relative to identically sized disjoint regions. We also show that in the overlap of DES and SDSS-III in Stripe 82, cross-correlating improves photo-$z$ parameter constraints by factors of $\sim 2$ to $\sim 12$ over internal photo-$z$ reconstructions.

Revised version, new table with absolute cosmological constraints. Accepted in Phys. Rev. D

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• Characterizing fast radio bursts through statistical cross-correlations
• Cosmological Information Contents on the Light-Cone
• The Impact of Anisotropic Redshift Distributions on Angular Clustering
• Analyzing Baryon Acoustic Oscillations in Sparse Spectroscopic Samples via Cross-Correlation with Dense Photometry
• Joint analyses of 2D CMB lensing and 3D galaxy clustering in the spherical Fourier-Bessel basis
• High resolution tomography for galaxy spectroscopic surveys with angular redshift fluctuations
• Optimizing galaxy samples for clustering measurements in photometric surveys
• Euclid preparation. Improving cosmological constraints using a new multi-tracer method with the spectroscopic and photometric samples
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• The Covariance of Photometric and Spectroscopic Two-Point Statistics: Implications for Cosmological Parameter Inference