Neural network based emulation of galaxy power spectrum covariances -- A reanalysis of BOSS DR12 data

TL;DR

This paper develops a neural network emulator to rapidly generate galaxy power spectrum covariances, enabling more accurate cosmological parameter estimation from galaxy survey data.

Contribution

The authors introduce a novel neural network architecture combining fully-connected and transformer layers to emulate galaxy power spectrum covariances across parameter space.

Findings

Emulator accurately predicts covariances over a large parameter range.

Re-analysis shows covariance variation affects cosmological constraints.

Emulator improves likelihood analysis accuracy and efficiency.

Abstract

We train neural networks to quickly generate redshift-space galaxy power spectrum covariances from a given parameter set (cosmology and galaxy bias). This covariance emulator utilizes a combination of traditional fully-connected network layers and transformer architecture to accurately predict covariance matrices for the high redshift, north galactic cap sample of the BOSS DR12 galaxy catalog. We run simulated likelihood analyses with emulated and brute-force computed covariances, and we quantify the network's performance via two different metrics: 1) difference in $\chi^2$ and 2) likelihood contours for simulated BOSS DR 12 analyses. We find that the emulator returns excellent results over a large parameter range. We then use our emulator to perform a re-analysis of the BOSS HighZ NGC galaxy power spectrum, and find that varying covariance with cosmology along with the model vector produces $\Omega_m = 0.276^{+0.013}_{-0.015}$, $H_0 = 70.2\pm 1.9$ km/s/Mpc, and $\sigma_8 = 0.674^{+0.058}_{-0.077}$. These constraints represent an average $0.46\sigma$ shift in best-fit values and a $5\%$ increase in constraining power compared to fixing the covariance matrix ($\Omega_m = 0.293\pm 0.017$, $H_0 = 70.3\pm 2.0$ km/s/Mpc, $\sigma_8 = 0.702^{+0.063}_{-0.075}$). This work demonstrates that emulators for more complex cosmological quantities than second-order statistics can be trained over a wide parameter range at sufficiently high accuracy to be implemented in realistic likelihood analyses.