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Home All issues Volume 708 (April 2026) A&A, 708 (2026) A344 Full HTML
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Table D.1.

Comparison of viscous cosmological models with standard ΛCDM.

Datasets AICi ΔAIC BICi ΔBIC DICi ΔDIC lnℰi lnℬ0i
ΛvCDM (m = 0)
PPS 1461.96 −1.93 1489.02 −7.34 1459.41 −0.6 −6.28 1.79
Base 1 1430.81 4.55 1457.76 −0.84 1430.52 2.52 −5.95 1.33
Base 1 + CC 1445.77 4.76 1472.82 −0.65 1445.29 3.31 −5.98 1.26
Base 1 + CC + R22 1463.00 1.75 1490.05 −3.66 1461.14 1.71 −6.17 1.18
Base 2 1506.52 2.12 1531.55 −3.31 1502.40 1.98 −6.34 1.40
Base 2 + CC 1520.30 1.68 1547.55 −3.77 1517.84 1.99 −6.31 1.31
Base 2 + CC + R22 1526.14 0.62 1553.39 −4.83 1522.84 1.62 −6.51 1.37
Base 3 1521.96 −0.82 1549.15 −6.26 1520.51 0.50 −8.29 2.06
Base 3 + CC 1536.91 −0.82 1564.20 −6.28 1535.48 0.46 −8.26 1.95
Base 3 + CC + R22 1547.12 −1.95 1574.42 −7.42 1545.06 −0.02 −8.55 2.21
ΛvCDM + ΩK (m = 0)
PPS 1463.72 −3.69 1496.20 −14.52 1459.62 −0.81 −8.77 4.28
Base 1 1429.36 6.00 1461.70 −4.78 1425.68 7.36 −8.87 4.25
Base 1 + CC 1445.17 5.36 1477.63 −5.46 1441.32 7.28 −8.93 4.21
Base 1 + CC + R22 1465.65 −0.90 1498.12 −11.73 1462.22 0.63 −9.27 4.28
Base 2 1506.81 −0.29 1539.39 −11.15 1503.93 0.45 −9.29 4.35
Base 2 + CC 1522.80 −0.82 1555.50 −11.72 1519.07 0.76 −9.20 4.20
Base 2 + CC + R22 1527.16 −0.40 1559.87 −11.31 1524.37 0.09 −9.54 4.40
Base 3 1524.06 −2.92 1556.69 −13.80 1522.36 −1.35 −13.34 7.11
Base 3 + CC 1538.91 −2.82 1571.66 −13.74 1537.29 −1.35 −13.36 7.05
Base 3 + CC + R22 1548.15 −2.98 1580.90 −13.90 1546.22 −1.18 −13.52 7.18
ΛvCDM (m free)
PPS 1463.78 −3.75 1496.26 −14.58 1459.43 −0.62 −5.01 0.52
Base 1 1428.83 6.53 1461.17 −4.25 1426.09 6.95 −5.60 0.98
Base 1 + CC 1443.90 6.63 1476.36 −4.19 1440.63 7.97 −5.57 0.85
Base 1 + CC + R22 1463.68 1.07 1496.15 −9.76 1459.87 2.98 −5.48 0.49
Base 2 1505.43 1.09 1538.01 −9.77 1502.09 2.29 −5.52 0.58
Base 2 + CC 1521.09 0.89 1553.79 −10.01 1517.09 2.74 −5.60 0.60
Base 2 + CC + R22 1527.76 −1.00 1560.46 −11.90 1523.25 1.21 −5.53 0.39
Base 3 1523.88 −2.74 1556.51 −13.62 1521.07 −0.06 −6.94 0.71
Base 3 + CC 1539.00 −2.91 1571.75 −13.83 1535.96 −1.85 −7.16 0.85
Base 3 + CC + R22 1549.17 −4.00 1581.93 −14.93 1545.36 −0.32 −7.07 0.73
ΛvCDM + ΩK (m free)
PPS 1465.76 −5.73 1503.65 −21.97 1459.41 −0.60 −7.49 3.00
Base 1 1430.83 4.53 1468.56 −11.64 1425.35 7.69 −7.74 3.12
Base 1 + CC 1445.98 4.55 1483.86 −11.69 1441.21 7.39 −7.72 3.00
Base 1 + CC + R22 1462.63 2.12 1500.51 −14.12 1460.85 2.00 −8.13 3.14
Base 2 1503.50 3.02 1541.52 −13.28 1488.85 15.53 −8.23 3.29
Base 2 + CC 1518.71 3.27 1556.86 −13.08 1518.12 1.71 −8.21 3.21
Base 2 + CC + R22 1522.26 4.50 1560.42 −11.86 1526.61 −2.15 −8.31 3.17
Base 3 1525.75 −4.61 1563.82 −20.93 1522.81 −1.80 −11.78 5.55
Base 3 + CC 1540.52 −4.43 1578.72 −20.80 1537.79 −1.85 −11.94 5.63
Base 3 + CC + R22 1549.44 −4.27 1587.64 −20.64 1546.38 −1.34 −11.89 5.55

Notes. We use information criteria (DIC, BIC, and AIC), Bayesian evidence (lnℰ), and Bayes factor (lnℬ0i). Here, ΔIC = ICΛCDM − ICi and lnℬ0i = lnℰΛCDM − lnℰi, where the index i denotes each proposed bulk viscous model. Values of ΔIC > 2 indicate a preference for bulk viscous model, while lnℬ0i > 1 favors the ΛCDM model.

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