CosmoForge. I. A unified framework for quadratic maximum likelihood power spectrum estimation and pixel-based likelihood analysis
Year: 2026
Type: article
Abstract: Optimal power spectrum estimation on the largest angular scales of the cosmic microwave background relies on the quadratic maximum likelihood (QML) estimator. Existing public implementations, however, each address only a subset of the problem, and none combines power spectrum estimation with a self-consistent pixel-space likelihood within a single framework. We present ̧f, a public Python framework that unifies QML power spectrum estimation and pixel-based Gaussian likelihood evaluation for spin-0 and spin-2 fields on the sphere, with general (non-diagonal) noise covariances. The framework is split into three installable packages: ç (infrastructure), (łmax^4) for arbitrary noise covariances, with (Fisher and QML estimation), and (pixel-space likelihood). A common interface exposes two interchangeable computation bases -- a harmonic basis built on the Sherman--Morrison--Woodbury identity and a direct pixel-space basis -- selecting whichever is cheaper for the configuration at hand. Exact algorithmic optimisations reduce the Fisher cost to mathcal O Numba JIT compilation of the hot kernels and MPI parallelisation of the likelihood scan. ̧f reproduces the Planck low-ell Fortran reference implementation across both the QML and pixel-space likelihood pipelines, consistently with double-precision arithmetic. Native multipole binning and three output normalisations (deconvolved, de-correlated, and window-convolved) are exposed through a single code path, and the same covariance infrastructure powers both QML estimation and likelihood evaluation. ̧f offers a general-purpose, modular, and validated tool for the optimal analysis of large-scale data on the sphere. It is publicly available, pip-installable, and extensible to observables other than the cosmic microwave background.
Source: Astronomy and Astrophysics
Authors: G. Galloni, L. Pagano
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,865
Funder: European Commission
OpenAlex ID: W7221701670