Theoretical Framework for Covariance Modeling in Multi-Tracer Cosmological Power Spectrum Measurements
Researchers have published a generalized analytical expression for the Gaussian covariance of multi-tracer power spectrum measurements, covering both real (even-parity) and complex (odd-parity) statistics. Multi-tracer analyses help mitigate cosmic variance, while parity-odd signatures can probe relativistic projection effects on cosmological scales, making accurate covariance modeling increasingly important for next-generation surveys. The work provides a computationally tractable alternative to expensive simulation-based covariance estimates, validated against Gaussian Monte Carlo simulations.
A new preprint submitted to arXiv presents a generalized theoretical framework for computing the Gaussian covariance of cross-correlation and multi-tracer power spectra in large-scale structure surveys. The authors extend previous results to handle both real (even-parity) and complex (even- and odd-parity) power spectra within a unified formalism, addressing a gap relevant to emerging analyses of parity-odd two-point statistics. The framework is first developed for a generic weighted estimator and then applied specifically to Legendre power spectrum multipoles and two-dimensional power spectra, recovering known limiting cases in each regime. Predictions are validated against Gaussian Monte Carlo simulations, and the Hermitian structure of the imaginary part of the covariance matrix is analyzed in detail. The work is motivated by the high computational cost of simulation-based covariance estimates and the growing scientific interest in multi-tracer techniques—which reduce cosmic variance—and relativistic projection effects accessible through parity-odd observables. Accurate covariance modeling is essential for maximally exploiting data from current and forthcoming galaxy surveys targeting large-scale clustering signals at unprecedented precision.
What's missing
The paper is a preprint and has not yet undergone peer review. The authors note the framework assumes Gaussian statistics; non-Gaussian contributions to the covariance (e.g., from mode coupling on nonlinear scales) are not addressed. The scope of validation is limited to Gaussian Monte Carlo simulations, leaving open how well the analytical predictions perform in the presence of realistic survey systematics, non-Gaussianity, or survey geometry effects such as the window function.
What different sources said
- arXiv astro-phCenter
Complex yet Hermitian: Gaussian covariance of cross-correlation and multi-tracer power spectra
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