A Gaussian Covariance Matrix for Joint Pre- and Post-Reconstruction Full-Shape Power Spectrum Analysis
Abstract
We apply the Gaussian covariance formalism to develop a semi-analytical covariance model for the joint analysis of pre-reconstruction, post-reconstruction, and cross full-shape galaxy power spectra. We model the reconstruction-reduced, scale-dependent cross shot noise using displacement-field statistics and introduce a new estimator that directly measures this term. Using the measured power spectra and the modeled shot-noise predictions as inputs, we construct the Gaussian covariance while accounting for correlations between the pre- and post-reconstruction density fields. We validate the resulting semi-analytical Gaussian covariance against mock catalogues. Using emulator-based parameter inference, we demonstrate that the semi-analytical Gaussian covariance adequately captures the dominant contribution to the covariance structure of the full data vector (Pℓpre, Pℓpost, Pℓcross). For the joint fit to these three power spectra, it yields cosmological constraints consistent with those obtained using the mock-based numerical covariance over the adopted fitting ranges: kmax=0.18 h Mpc−1 for Ppre and Ppost, and kmax=0.12 h Mpc−1 for Pcross.
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BibTeX
@misc{wang2026gaussian,
title = {{A Gaussian Covariance Matrix for Joint Pre- and Post-Reconstruction Full-Shape Power Spectrum Analysis}},
author = {Yuting Wang and Ruiyang Zhao and Gong-Bo Zhao and Kazuya Koyama},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.05504},
eprint = {2608.05504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.05504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Gaussian Covariance Matrix for Joint Pre- and Post-Reconstruction Full-Shape Power Spectrum Analysis
AU - Yuting Wang
AU - Ruiyang Zhao
AU - Gong-Bo Zhao
AU - Kazuya Koyama
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2608.05504
UR - https://arxiv.org/abs/2608.05504
AB - We apply the Gaussian covariance formalism to develop a semi-analytical covariance model for the joint analysis of pre-reconstruction, post-reconstruction, and cross full-shape galaxy power spectra. We model the reconstruction-reduced, scale-dependent cross shot noise using displacement-field statistics and introduce a new estimator that directly measures this term. Using the measured power spectra and the modeled shot-noise predictions as inputs, we construct the Gaussian covariance while accounting for correlations between the pre- and post-reconstruction density fields. We validate the resulting semi-analytical Gaussian covariance against mock catalogues. Using emulator-based parameter inference, we demonstrate that the semi-analytical Gaussian covariance adequately captures the dominant contribution to the covariance structure of the full data vector (P_ℓ^pre, P_ℓ^post, P_ℓ^cross). For the joint fit to these three power spectra, it yields cosmological constraints consistent with those obtained using the mock-based numerical covariance over the adopted fitting ranges: k_max=0.18 h Mpc^−1 for P_pre and P_post, and k_max=0.12 h Mpc^−1 for P_cross.
ER -