Accelerating the standard siren method: Improved constraints on modified gravitational-wave propagation with future data

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Volume 702 (October 2025)

A&A, 702 (2025) A244

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Table 2.

Constraints on H₀ and MG hyperparameters.

Catalog	`spec-z`						`photo-z`

	H₀		Ξ₀		n		H₀		Ξ₀		n
MG0.6	$70 . 11_{- 0.61}^{+ 0.61}$ $70.11^{+0.61}_{-0.61}$	(0.9%)	⋅		⋅		$71 . 9_{- 3.7}^{+ 3.8}$ $71.9^{+3.8}_{-3.7}$	(5.2%)	⋅		⋅
	⋅		$0 . 56_{- 0.13}^{+ 0.11}$ $0.56^{+0.11}_{-0.13}$	(22%)	$2 . 42_{- 0.68}^{+ 0.79}$ $2.42^{+0.79}_{-0.68}$	(30%)	⋅		$0 . 60_{- 0.14}^{+ 0.15}$ $0.60^{+0.15}_{-0.14}$	(24%)	$1 . 46_{- 0.34}^{+ 0.81}$ $1.46^{+0.81}_{-0.34}$	(39%)
	$69 . 3_{- 1.4}^{+ 1.2}$ $69.3^{+1.2}_{-1.4}$	(1.9%)	$0 . 54_{- 0.14}^{+ 0.10}$ $0.54^{+0.10}_{-0.14}$	(22%)	$2 . 35_{- 0.80}^{+ 1.08}$ $2.35^{+1.08}_{-0.80}$	(40%)	$80_{- 13}^{+ 18}$ $80^{+18}_{-13}$	(19%)	$0 . 70_{- 0.17}^{+ 0.25}$ $0.70^{+0.25}_{-0.17}$	(30%)	$2 . 9_{- 1.3}^{+ 1.4}$ $2.9^{+1.4}_{-1.3}$	(47%)

GR	$70 . 45_{- 0.56}^{+ 0.59}$ $70.45^{+0.59}_{-0.56}$	(0.82%)	⋅		⋅		$71 . 4_{- 4.3}^{+ 4.4}$ $71.4^{+4.4}_{-4.3}$	(6.1%)	⋅		⋅
	⋅		$0 . 99_{- 0.08}^{+ 0.08}$ $0.99^{+0.08}_{-0.08}$	(8%)	$2 . 5_{- 1.1}^{+ 1.6}$ $2.5^{+1.6}_{-1.1}$	(54%)	⋅		$1 . 00_{- 0.10}^{+ 0.12}$ $1.00^{+0.12}_{-0.10}$	(11%)	$2 . 6_{- 1.2}^{+ 1.6}$ $2.6^{+1.6}_{-1.2}$	(54%)
	$70 . 7_{- 2.1}^{+ 2.4}$ $70.7^{+2.4}_{-2.1}$	(3.2%)	$1 . 00_{- 0.07}^{+ 0.08}$ $1.00^{+0.08}_{-0.07}$	(7.5%)	$2 . 8_{- 1.3}^{+ 1.5}$ $2.8^{+1.5}_{-1.3}$	(50%)	$82_{- 15}^{+ 30}$ $82^{+30}_{-15}$	(27%)	$1 . 27_{- 0.36}^{+ 0.67}$ $1.27^{+0.67}_{-0.36}$	(41%)	3.1 ± 1.4	(45%)

MG1.8	$70 . 4_{- 0.5}^{+ 0.5}$ $70.4^{+0.5}_{-0.5}$	(0.72%)	⋅		⋅		$72 . 3_{- 4.6}^{+ 4.9}$ $72.3^{+4.9}_{-4.6}$	(6.5%)	⋅		⋅
MG1.8	⋅		$1 . 79_{- 0.19}^{+ 0.36}$ $1.79^{+0.36}_{-0.19}$	(15%)	$2 . 37_{- 0.82}^{+ 0.99}$ $2.37^{+0.99}_{-0.82}$	(38%)	⋅		$1 . 73_{- 0.23}^{+ 0.38}$ $1.73^{+0.38}_{-0.23}$	(18%)	$2 . 5_{- 1.1}^{+ 1.5}$ $2.5^{+1.5}_{-1.1}$	(52%)
	$73 . 0_{- 3.5}^{+ 4.1}$ $73.0^{+4.1}_{-3.5}$	(5.2%)	$1 . 79_{- 0.15}^{+ 0.20}$ $1.79^{+0.20}_{-0.15}$	(10%)	$3 . 5_{- 1.4}^{+ 1.1}$ $3.5^{+1.1}_{-1.4}$	(36%)	$70_{- 13}^{+ 21}$ $70^{+21}_{-13}$	(24%)	$1 . 78_{- 0.47}^{+ 0.76}$ $1.78^{+0.76}_{-0.47}$	(35%)	$3 . 5_{- 1.5}^{+ 1.1}$ $3.5^{+1.1}_{-1.5}$	(37%)

Notes. The central values are the median of the 1D marginalized distributions. Errors are reported as the 68% C.L. around the median. The percentage error shown is the mean between the upper and lower percentage errors. For each catalog: the first raw shows results when inferring only H₀ and population hyperparameters, keeping MG hyperparameters fixed; the second raw infers MG and population hyperparameters only, keeping H₀ fixed; the last row infers all hyperparameters.

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