Comment on "Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev--Zeldovich Effect''
Abstract
Gallardo et al. [Phys. Rev. Lett. \textbf{136}, 151002 (2026)] constrain the index of the force law g∝ r−n with pairwise kinematic Sunyaev--Zeldovich measurements, n=2.1±0.3, and exclude the deep-MOND value n=1 at 3.3σ. The exclusion does not follow from their calculation. Their templates for n≠2 [their Eq.~(8)] raise the pair-averaged Newtonian acceleration to the power n/2, whereas the pair average of the pointwise law [their Eq.~(30) for deep MOND] is the average of the transformed field; the step that identifies the two attributes to the three-point function a correction that is of second order and not small. In a Gaussian linear field with linearly biased tracers, Gaussian integration by parts shows that the correctly averaged template is exactly proportional to the Newtonian one, with a constant that the analysis absorbs into the mean optical depth. Gaussian realizations with peak-selected tracers find the same proportionality to within 2\% (0.5\% for the fiducial selection), and refitting the data of the Letter with the resulting template gives χ2=20.1--$20.2$, against $20.1$ for the Newtonian template and $33.8$ for Eq.~(8): in every controlled case examined the data do not discriminate between n=1 and n=2, and the 3.3σ exclusion, with the 10σ forecast that rescales it, rests on the order in which the average and the power were taken. What a self-consistent MOND cosmology predicts for this observable is a separate question, which the Letter does not address.
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BibTeX
@misc{melchiorri2026comment,
title = {{Comment on "Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev--Zeldovich Effect''}},
author = {Alessandro Melchiorri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34437},
eprint = {2610.34437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34437},
}
RIS
TY - UNPB
TI - Comment on "Test of the Gravitational Force Law on Cosmological Scales Using the Kinematic Sunyaev--Zeldovich Effect''
AU - Alessandro Melchiorri
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34437
UR - https://arxiv.org/abs/2610.34437
AB - Gallardo et al. [Phys. Rev. Lett. \textbf{136}, 151002 (2026)] constrain the index of the force law g∝ r^−n with pairwise kinematic Sunyaev--Zeldovich measurements, n=2.1±0.3, and exclude the deep-MOND value n=1 at 3.3σ. The exclusion does not follow from their calculation. Their templates for n≠2 [their Eq.~(8)] raise the pair-averaged Newtonian acceleration to the power n/2, whereas the pair average of the pointwise law [their Eq.~(30) for deep MOND] is the average of the transformed field; the step that identifies the two attributes to the three-point function a correction that is of second order and not small. In a Gaussian linear field with linearly biased tracers, Gaussian integration by parts shows that the correctly averaged template is exactly proportional to the Newtonian one, with a constant that the analysis absorbs into the mean optical depth. Gaussian realizations with peak-selected tracers find the same proportionality to within 2\% (0.5\% for the fiducial selection), and refitting the data of the Letter with the resulting template gives χ^2=20.1--$20.2$, against $20.1$ for the Newtonian template and $33.8$ for Eq.~(8): in every controlled case examined the data do not discriminate between n=1 and n=2, and the 3.3σ exclusion, with the 10σ forecast that rescales it, rests on the order in which the average and the power were taken. What a self-consistent MOND cosmology predicts for this observable is a separate question, which the Letter does not address.
ER -