CosmoForge II. An exact treatment of arbitrary linear filters in quadratic maximum-likelihood power spectrum estimation
Abstract
Ground-based cosmic microwave background (CMB) experiments filter their time-ordered data to remove 1/f noise and ground pickup, which removes or mixes the large angular scales where primordial B modes peak. A common remedy is a pseudo-Cℓ estimator with harmonic B-purification and a transfer function measured from simulations. Another applies it after a matrix-based E/B purification of the maps. We extend the quadratic maximum-likelihood (QML) estimator of CosmoForge to filtered maps, treating the filter exactly: a linear filter conjugates the estimator's ingredients without altering its structure. The same holds for the pixel-based likelihood of CosmoForge, which gives the smallest error bar achievable on the same maps. We compare all methods in a simplified setup under several map-level filters through the error bars on bandpowers and on the tensor-to-scalar ratio r. QML sits $2$ to 4% above the pixel-likelihood bound on σ(r) in every filter state. At low noise, the pure pseudo-Cℓ σ(r) is $1.21$ times QML's without filtering, $3.0$ times under a scan filter along stripes of constant declination, and $3.7$ times under one from a toy constant-elevation scan. The matrix-purified pseudo-Cℓ σ(r) is at most $1.03$ times QML's except under the constant-elevation filters, where it reaches $1.10$. These factors shrink towards unity at higher noise. The pure pseudo-Cℓ gap comes from apodisation and from harmonic E/B separation; pixel-space separation closes it, except under the constant-elevation filters, which attenuate modes rather than remove them and widen the gap. QML stays within a few per cent of the optimal error bars without the tuning and simulated transfer functions of the pseudo-Cℓ pipelines. Thus, CosmoForge provides a robust framework for power-spectrum estimation and inference on filtered maps. (Abridged)
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BibTeX
@misc{galloni2026cosmoforge,
title = {{CosmoForge II. An exact treatment of arbitrary linear filters in quadratic maximum-likelihood power spectrum estimation}},
author = {Giacomo Galloni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18012},
eprint = {2610.18012},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18012},
}
RIS
TY - UNPB
TI - CosmoForge II. An exact treatment of arbitrary linear filters in quadratic maximum-likelihood power spectrum estimation
AU - Giacomo Galloni
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18012
UR - https://arxiv.org/abs/2610.18012
AB - Ground-based cosmic microwave background (CMB) experiments filter their time-ordered data to remove 1/f noise and ground pickup, which removes or mixes the large angular scales where primordial B modes peak. A common remedy is a pseudo-C_ℓ estimator with harmonic B-purification and a transfer function measured from simulations. Another applies it after a matrix-based E/B purification of the maps. We extend the quadratic maximum-likelihood (QML) estimator of CosmoForge to filtered maps, treating the filter exactly: a linear filter conjugates the estimator's ingredients without altering its structure. The same holds for the pixel-based likelihood of CosmoForge, which gives the smallest error bar achievable on the same maps. We compare all methods in a simplified setup under several map-level filters through the error bars on bandpowers and on the tensor-to-scalar ratio r. QML sits $2$ to 4% above the pixel-likelihood bound on σ(r) in every filter state. At low noise, the pure pseudo-C_ℓ σ(r) is $1.21$ times QML's without filtering, $3.0$ times under a scan filter along stripes of constant declination, and $3.7$ times under one from a toy constant-elevation scan. The matrix-purified pseudo-C_ℓ σ(r) is at most $1.03$ times QML's except under the constant-elevation filters, where it reaches $1.10$. These factors shrink towards unity at higher noise. The pure pseudo-C_ℓ gap comes from apodisation and from harmonic E/B separation; pixel-space separation closes it, except under the constant-elevation filters, which attenuate modes rather than remove them and widen the gap. QML stays within a few per cent of the optimal error bars without the tuning and simulated transfer functions of the pseudo-C_ℓ pipelines. Thus, CosmoForge provides a robust framework for power-spectrum estimation and inference on filtered maps. (Abridged)
ER -