Table 4.
Best-fit values with the corresponding 1σ error bars for the cosmological and nuisance parameters of the third case: SNIa, BAO, and CMB data.
Case | Model | h1 | h2 | h3 | h4 | h5 | h6 | H0 | rd | Ωm | 102ωb | α | β | M | ΔM | zCMB | zdrag | ϵ | δ | χ2/d.o.f | P(χ2, ν) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ΛCDM | − | − | − | − | − | − | 69.15 ± 0.93 | 146.3 ± 1.4 | 0.293 ± 0.011 | 2.265 ± 0.025 | 0.1412 ± 0.0066 | 3.102 ± 0.080 | 24.110 ± 0.018 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | − | − | 698.10/751 | 0.916 | |
SNIa+BAO free rd+CMB | Splines | 1.050 ± 0.021 | 1.133 ± 0.020 | 1.387 ± 0.035 | 1.601 ± 0.082 | 2.13 ± 0.16 | 3.44 ± 0.10 | 68.5 ± 1.7 | 146.8 ± 2.7 | 0.299 ± 0.016 | 2.263 ± 0.029 | 0.1410 ± 0.0066 | 3.098 ± 0.079 | 24.120 ± 0.031 | −0.070 ± 0.023 | 1090.00 ± 0.22 | − | − | − | 696.21/745 | 0.899 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.28 ± 0.15 | 3.788 ± 0.095 | 62.6 ± 1.1 | 146.3 ± 2.4 | 0.358 ± 0.014 | 2.264 ± 0.029 | 0.1382 ± 0.0066 | 3.073 ± 0.080 | 24.230 ± 0.017 | −0.077 ± 0.023 | 1090.00 ± 0.23 | − | − | − | 739.13/749 | 0.594 | |
ΛCDM | − | − | − | − | − | − | 69.13 ± 0.97 | 146.4 ± 1.5 | 0.294 ± 0.012 | 2.264 ± 0.025 | 0.1413 ± 0.0066 | 3.103 ± 0.081 | 24.110 ± 0.056 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.005 ± 0.074 | 0.20 ± 0.91 | 698.09/749 | 0.908 | |
SNIa+ev+BAO free rd+CMB | Splines | 1.048 ± 0.021 | 1.151 ± 0.023 | 1.414 ± 0.039 | 1.70 ± 0.10 | 2.17 ± 0.16 | 3.48 ± 0.10 | 67.2 ± 1.7 | 147.7 ± 2.6 | 0.311 ± 0.017 | 2.263 ± 0.029 | 0.1413 ± 0.0066 | 3.101 ± 0.081 | 24.110 ± 0.031 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.103 ± 0.065 | 2.0 ± 1.5 | 693.81/743 | 0.901 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.35 ± 0.17 | 3.777 ± 0.093 | 62.2 ± 1.1 | 147.1 ± 2.5 | 0.362 ± 0.015 | 2.263 ± 0.029 | 0.1416 ± 0.0066 | 3.104 ± 0.081 | 24.050 ± 0.090 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.322 ± 0.075 | 0.41 ± 0.24 | 698.30/747 | 0.898 | |
ΛCDM | − | − | − | − | − | − | 68.77 ± 0.73 | 147.20 ± 0.63 | 0.2977 ± 0.0090 | 2.256 ± 0.022 | 0.1412 ± 0.0066 | 3.101 ± 0.080 | 24.110 ± 0.018 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | − | − | 698.52/752 | 0.919 | |
SNIa+BAO prior rd+CMB | Splines | 1.050 ± 0.021 | 1.133 ± 0.020 | 1.387 ± 0.034 | 1.603 ± 0.079 | 2.153 ± 0.098 | 3.44 ± 0.10 | 68.3 ± 1.2 | 147.40 ± 0.68 | 0.302 ± 0.012 | 2.262 ± 0.028 | 0.1410 ± 0.0066 | 3.098 ± 0.081 | 24.120 ± 0.030 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | − | − | 696.25/746 | 0.903 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.344 ± 0.089 | 3.786 ± 0.095 | 62.20 ± 0.54 | 147.30 ± 0.67 | 0.3632 ± 0.0086 | 2.261 ± 0.028 | 0.1382 ± 0.0066 | 3.073 ± 0.080 | 24.230 ± 0.017 | −0.077 ± 0.023 | 1090.00 ± 0.23 | − | − | − | 739.31/750 | 0.603 | |
ΛCDM | − | − | − | − | − | − | 68.74 ± 0.69 | 147.20 ± 0.59 | 0.2981 ± 0.0086 | 2.256 ± 0.021 | 0.1413 ± 0.0066 | 3.102 ± 0.081 | 24.110 ± 0.029 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.006 ± 0.049 | 0.5 ± 1.0 | 698.51/750 | 0.911 | |
SNIa+ev+BAO prior rd+CMB | Splines | 1.048 ± 0.029 | 1.151 ± 0.024 | 1.413 ± 0.041 | 1.693 ± 0.098 | 2.16 ± 0.10 | 3.48 ± 0.11 | 67.4 ± 1.4 | 147.40 ± 0.68 | 0.309 ± 0.014 | 2.264 ± 0.028 | 0.1413 ± 0.0066 | 3.100 ± 0.081 | 24.110 ± 0.038 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.101 ± 0.064 | 2.0 ± 1.5 | 693.83/744 | 0.906 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.362 ± 0.091 | 3.777 ± 0.093 | 62.13 ± 0.55 | 147.40 ± 0.68 | 0.3638 ± 0.0086 | 2.263 ± 0.028 | 0.1416 ± 0.0066 | 3.104 ± 0.081 | 24.05 ± 0.10 | −0.070 ± 0.023 | 1090.00 ± 0.23 | − | 0.321 ± 0.083 | 0.41 ± 0.25 | 698.31/748 | 0.903 | |
ΛCDM | − | − | − | − | − | − | 68.62 ± 0.60 | − | 0.2997 ± 0.0072 | 2.255 ± 0.022 | 0.1411 ± 0.0066 | 3.100 ± 0.080 | 24.110 ± 0.018 | −0.070 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | − | − | 698.62/752 | 0.918 | |
SNIa+BAO compute rd+CMB | Splines | 1.050 ± 0.020 | 1.133 ± 0.020 | 1.386 ± 0.034 | 1.604 ± 0.079 | 2.158 ± 0.098 | 3.44 ± 0.10 | 68.2 ± 1.2 | − | 0.302 ± 0.011 | 2.262 ± 0.028 | 0.1410 ± 0.0066 | 3.098 ± 0.081 | 24.120 ± 0.030 | −0.070 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | − | − | 696.27/746 | 0.903 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.350 ± 0.089 | 3.786 ± 0.095 | 62.15 ± 0.50 | − | 0.3642 ± 0.0066 | 2.260 ± 0.028 | 0.1382 ± 0.0066 | 3.073 ± 0.080 | 24.230 ± 0.017 | −0.077 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | − | − | 739.35/750 | 0.602 | |
ΛCDM | − | − | − | − | − | − | 68.60 ± 0.61 | − | 0.3000 ± 0.0074 | 2.255 ± 0.022 | 0.1413 ± 0.0066 | 3.102 ± 0.081 | 24.100 ± 0.056 | −0.070 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | 0.017 ± 0.073 | 0.2 ± 1.8 | 698.56/750 | 0.910 | |
SNIa+ev+BAO compute rd+CMB | Splines | 1.048 ± 0.027 | 1.151 ± 0.024 | 1.413 ± 0.041 | 1.694 ± 0.097 | 2.163 ± 0.099 | 3.48 ± 0.11 | 67.3 ± 1.4 | − | 0.310 ± 0.013 | 2.264 ± 0.028 | 0.1413 ± 0.0066 | 3.100 ± 0.081 | 24.110 ± 0.036 | −0.070 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | 0.102 ± 0.064 | 2.0 ± 1.5 | 693.82/744 | 0.906 |
CS (4 knots) | (1.10) | (1.25) | (1.57) | (1.80) | 2.369 ± 0.091 | 3.776 ± 0.094 | 62.08 ± 0.51 | − | 0.3645 ± 0.0066 | 2.262 ± 0.028 | 0.1416 ± 0.0066 | 3.104 ± 0.081 | 24.050 ± 0.092 | −0.070 ± 0.023 | 1090.00 ± 0.23 | 1060.00 ± 0.29 | 0.322 ± 0.076 | 0.41 ± 0.24 | 698.32/748 | 0.903 |
Notes. The values in parentheses show the fixed knots. The values of ΛCDM are added as a reference. The reduced χ2 and the probability P(χ2, ν) are also provided for the different models. H0 is expressed in km s−1 Mpc−1, and rd in Mpc.
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