COBRA: Optimal Factorization of Cosmological Observables

TL;DR

COBRA is a new framework that efficiently decomposes cosmological observables into basis functions, enabling rapid and precise computations for large-scale structure analysis, significantly improving over previous methods.

Contribution

The paper introduces COBRA, a novel basis decomposition method that separates scale dependence from cosmological parameters, allowing fast and accurate computation of observables with minimal basis terms.

Findings

Reproduces Boltzmann solver calculations to 0.1% with 12 basis terms

Achieves 0.02% precision in pure ΛCDM scenario

Enables ~4000 model evaluations per second for the galaxy power spectrum

Abstract

We introduce COBRA (Cosmology with Optimally factorized Bases of Radial Approximants), a novel framework for rapid computation of large-scale structure observables. COBRA separates scale dependence from cosmological parameters in the linear matter power spectrum while also minimising the number of necessary basis terms $N_b$, thus enabling direct and efficient computation of derived and nonlinear observables. Moreover, the dependence on cosmological parameters is efficiently approximated using radial basis function interpolation. We apply our framework to decompose the linear matter power spectrum in the standard $\Lambda$CDM scenario, as well as by adding curvature, dynamical dark energy and massive neutrinos, covering all redshifts relevant for Stage IV surveys. With only a dozen basis terms $N_b$, COBRA reproduces exact Boltzmann solver calculations to $\sim 0.1\%$ precision, which improves further to $0.02\%$ in the pure $\Lambda$CDM scenario. Using our decomposition, we recast the one-loop redshift space galaxy power spectrum in a separable minimal-basis form, enabling $\sim 4000$ model evaluations per second at $0.02\%$ precision on a single thread. This constitutes a considerable improvement over previously existing methods (e.g., FFTLog) opening a window for efficient computations of higher loop and higher order correlators involving multiple powers of the linear matter power spectra. The resulting factorisation can also be utilised in clustering, weak lensing and CMB analyses. Our implementation will be made public upon publication.