TDCOSMO 2025: Cosmological constraints from strong lensing time delays

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Volume 704 (December 2025)

A&A, 704 (2025) A63

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Table 7.

Cosmological parameters for extensions to the ΛCDM model, from time-delay cosmography alone, or combined with other probes.

Model	Experiments/datasets	H₀ [km s⁻¹ Mpc⁻¹]	Ω_m	Ω_k	w or w₀	w_a
UoΛCDM	TDCOSMO	$77 . 1_{- 4.1}^{+ 4.9}$ $77.1^{+4.9}_{-4.1}$	$0 . 229_{- 0.132}^{+ 0.151}$ $0.229^{+0.151}_{-0.132}$	$- 0 . 117_{- 0.245}^{+ 0.305}$ $-0.117^{+0.305}_{-0.245}$	–	–
oΛLCDM	TDCOSMO + Planck	$65 . 2_{- 2.3}^{+ 1.8}$ $65.2^{+1.8}_{-2.3}$	$0 . 338_{- 0.018}^{+ 0.030}$ $0.338^{+0.030}_{-0.018}$	$- 0 . 006_{- 0.006}^{+ 0.005}$ $-0.006^{+0.005}_{-0.006}$	–	–

UwCDM	TDCOSMO	$78 . 0_{- 7.3}^{+ 6.6}$ $78.0^{+6.6}_{-7.3}$	$0 . 178_{- 0.091}^{+ 0.194}$ $0.178^{+0.194}_{-0.091}$	–	$- 1 . 12_{- 0.27}^{+ 0.44}$ $-1.12^{+0.44}_{-0.27}$	–
wCDM1	TDCOSMO + Planck	$79 . 7_{- 4.3}^{+ 3.2}$ $79.7^{+3.2}_{-4.3}$	$0 . 225_{- 0.017}^{+ 0.027}$ $0.225^{+0.027}_{-0.017}$	–	$- 1 . 38_{- 0.08}^{+ 0.13}$ $-1.38^{+0.13}_{-0.08}$	–
wCDM2	TDCOSMO + DESI BAO	$74 . 0_{- 3.6}^{+ 3.4}$ $74.0^{+3.4}_{-3.6}$	$0 . 296_{- 0.008}^{+ 0.008}$ $0.296^{+0.008}_{-0.008}$	–	$- 0 . 93_{- 0.09}^{+ 0.08}$ $-0.93^{+0.08}_{-0.09}$	–
wCDM3	TDCOSMO + Pantheon+	$73 . 7_{- 3.1}^{+ 3.5}$ $73.7^{+3.5}_{-3.1}$	$0 . 277_{- 0.083}^{+ 0.072}$ $0.277^{+0.072}_{-0.083}$	–	$- 0 . 86_{- 0.18}^{+ 0.14}$ $-0.86^{+0.14}_{-0.18}$	–

Uw₀w_aCDM	TDCOSMO	$80 . 9_{- 8.0}^{+ 11.2}$ $80.9^{+11.2}_{-8.0}$	$0 . 203_{- 0.112}^{+ 0.171}$ $0.203^{+0.171}_{-0.112}$	–	$- 0 . 89_{- 0.43}^{+ 0.55}$ $-0.89^{+0.55}_{-0.43}$	$- 5 . 23_{- 3.31}^{+ 4.55}$ $-5.23^{+4.55}_{-3.31}$
w₀w_aCDM1	TDCOSMO + Planck	$65 . 9_{- 2.4}^{+ 2.7}$ $65.9^{+2.7}_{-2.4}$	$0 . 333_{- 0.027}^{+ 0.024}$ $0.333^{+0.024}_{-0.027}$	–	$- 0 . 64_{- 0.30}^{+ 0.28}$ $-0.64^{+0.28}_{-0.30}$	$- 1 . 20_{- 0.81}^{+ 0.84}$ $-1.20^{+0.84}_{-0.81}$
w₀w_aCDM2	TDCOSMO + DESI BAO	$70 . 4_{- 3.7}^{+ 5.5}$ $70.4^{+5.5}_{-3.7}$	$0 . 348_{- 0.066}^{+ 0.046}$ $0.348^{+0.046}_{-0.066}$	–	$- 0 . 54_{- 0.45}^{+ 0.41}$ $-0.54^{+0.41}_{-0.45}$	$- 1 . 50_{- 1.43}^{+ 1.77}$ $-1.50^{+1.77}_{-1.43}$
w₀w_aCDM3	TDCOSMO + Pantheon+	$74 . 7_{- 3.8}^{+ 3.3}$ $74.7^{+3.3}_{-3.8}$	$0 . 359_{- 0.147}^{+ 0.068}$ $0.359^{+0.068}_{-0.147}$	–	$- 0 . 90_{- 0.16}^{+ 0.14}$ $-0.90^{+0.14}_{-0.16}$	$- 0 . 79_{- 1.85}^{+ 1.30}$ $-0.79^{+1.30}_{-1.85}$
w₀w_aCDM4	TDCOSMO + DESI BAO + Pantheon+	$73 . 2_{- 3.0}^{+ 4.0}$ $73.2^{+4.0}_{-3.0}$	$0 . 303_{- 0.021}^{+ 0.016}$ $0.303^{+0.016}_{-0.021}$	–	$- 0 . 89_{- 0.05}^{+ 0.06}$ $-0.89^{+0.06}_{-0.05}$	$- 0 . 20_{- 0.45}^{+ 0.49}$ $-0.20^{+0.49}_{-0.45}$

Uw_ϕCDM	TDCOSMO	$75 . 9_{- 7.8}^{+ 6.8}$ $75.9^{+6.8}_{-7.8}$	$0 . 196_{- 0.098}^{+ 0.162}$ $0.196^{+0.162}_{-0.098}$	–	$- 0 . 95_{- 0.39}^{+ 0.59}$ $-0.95^{+0.59}_{-0.39}$	–
w_ϕCDM1	TDCOSMO + DESI BAO	$73 . 5_{- 3.1}^{+ 3.6}$ $73.5^{+3.6}_{-3.1}$	$0 . 305_{- 0.013}^{+ 0.012}$ $0.305^{+0.012}_{-0.013}$	–	$- 0 . 86_{- 0.13}^{+ 0.11}$ $-0.86^{+0.11}_{-0.13}$	–
w_ϕCDM2	TDCOSMO + Pantheon+	$73 . 8_{- 3.3}^{+ 3.3}$ $73.8^{+3.3}_{-3.3}$	$0 . 313_{- 0.042}^{+ 0.041}$ $0.313^{+0.041}_{-0.042}$	–	$- 0 . 92_{- 0.13}^{+ 0.11}$ $-0.92^{+0.11}_{-0.13}$	–

Notes. Reported values are medians, with errors corresponding to the 16th and 84th percentiles. In this table, we utilized the full strong lensing data set, which includes TDCOSMO-2025, SLACS, and SL2S lenses.

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