An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

TL;DR

This paper introduces a simple analytic model for the covariance between pre- and post-reconstruction galaxy clustering measurements, validated against simulations, facilitating efficient joint analyses in galaxy surveys.

Contribution

The authors develop and validate an analytic approximation for the cross-covariance between pre- and post-reconstruction galaxy clustering statistics, enabling faster and more efficient cosmological analyses.

Findings

Analytic model agrees well with simulations across survey configurations.

Pre-post covariance is small, allowing approximate treatments in cosmological inference.

Model simplifies covariance estimation for future galaxy surveys.

Abstract

We present a simple analytic approximation for the covariance between pre-reconstruction galaxy power spectrum measurements and post-reconstruction two-point correlation functions. This cross-covariance is essential for joint analyses that combine full-shape clustering information with baryon acoustic oscillation (BAO) measurements, as commonly performed in modern spectroscopic surveys. Our model builds on the disconnected contribution to the covariance and accounts for the damping of correlations due to the BAO reconstruction process. We validate our analytic prescription against numerical simulations from the Dark Energy Spectroscopic Instrument (DESI), testing both idealized cubic geometries and realistic survey configurations including complex footprints and fiber assignment effects. Despite neglecting survey window functions in the analytic calculation, we find excellent agreement with simulation-based covariances and demonstrate that cosmological parameter constraints are virtually unchanged when using our approximation. Our results show that the pre-post cross-covariance is sufficiently small that even approximate treatments are adequate for cosmological inference, opening a pathway toward fully analytic covariance matrices for next-generation galaxy surveys.