68 per cent and 95 per cent confidence level parameter constraints from the MCMC analysis of SN+OHD+BAO data for the fourth-order Taylor, (2,2) Padé and (2,1) rational Chebyshev polynomial approximations of the luminosity distance. H0 values are given in units of km s−1 Mpc−1, while rd values in units of Mpc.
| Parameter . | Taylor . | Padé . | Rational Chebyshev . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . |
| H0 | 65.80 | |$^{+2.09}_{-2.11}$| | |$^{+4.22}_{-4.00}$| | 64.94 | |$^{+2.11}_{-2.02}$| | |$^{+4.12}_{-4.13}$| | 64.95 | |$^{+1.89}_{-1.94}$| | |$^{+3.77}_{-3.77}$| |
| q0 | −0.276 | |$^{+0.043}_{-0.049}$| | |$^{+0.093}_{-0.091}$| | −0.285 | |$^{+0.040}_{-0.046}$| | |$^{+0.087}_{-0.084}$| | −0.278 | |$^{+0.021}_{-0.021}$| | |$^{+0.041}_{-0.042}$| |
| j0 | −0.023 | |$^{+0.317}_{-0.397}$| | |$^{+0.748}_{-0.685}$| | 0.545 | |$^{+0.463}_{-0.652}$| | |$^{+1.135}_{-1.025}$| | 1.585 | |$^{+0.497}_{-0.914}$| | |$^{+1.594}_{-1.453}$| |
| s0 | −0.745 | |$^{+0.196}_{-0.284}$| | |$^{+0.564}_{-0.487}$| | 0.118 | |$^{+0.451}_{-1.600}$| | |$^{+3.422}_{-1.921}$| | 1.041 | |$^{+1.183}_{-1.784}$| | |$^{+3.388}_{-3.087}$| |
| M | −19.16 | |$^{+0.07}_{-0.07}$| | |$^{+0.14}_{-0.14}$| | −19.03 | |$^{+0.02}_{-0.02}$| | |$^{+0.05}_{-0.05}$| | −19.17 | |$^{+0.07}_{-0.07}$| | |$^{+0.13}_{-0.13}$| |
| ΔM | −0.054 | |$^{+0.023}_{-0.022}$| | |$^{+0.044}_{-0.045}$| | −0.054 | |$^{+0.022}_{-0.023}$| | |$^{+0.045}_{-0.045}$| | −0.050 | |$^{+0.022}_{-0.022}$| | |$^{+0.044}_{-0.045}$| |
| α | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.130 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| |
| β | 2.624 | |$^{+0.071}_{-0.068}$| | |$^{+0.136}_{-0.140}$| | 2.625 | |$^{+0.065}_{-0.069}$| | |$^{+0.137}_{-0.135}$| | 2.667 | |$^{+0.068}_{-0.069}$| | |$^{+0.137}_{-0.135}$| |
| rd | 149.2 | |$^{+3.7}_{-4.1}$| | |$^{+7.7}_{-7.5}$| | 148.6 | |$^{+3.5}_{-3.8}$| | |$^{+7.5}_{-7.1}$| | 147.2 | |$^{+3.7}_{-4.0}$| | |$^{+7.8}_{-7.5}$| |
| Parameter . | Taylor . | Padé . | Rational Chebyshev . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . |
| H0 | 65.80 | |$^{+2.09}_{-2.11}$| | |$^{+4.22}_{-4.00}$| | 64.94 | |$^{+2.11}_{-2.02}$| | |$^{+4.12}_{-4.13}$| | 64.95 | |$^{+1.89}_{-1.94}$| | |$^{+3.77}_{-3.77}$| |
| q0 | −0.276 | |$^{+0.043}_{-0.049}$| | |$^{+0.093}_{-0.091}$| | −0.285 | |$^{+0.040}_{-0.046}$| | |$^{+0.087}_{-0.084}$| | −0.278 | |$^{+0.021}_{-0.021}$| | |$^{+0.041}_{-0.042}$| |
| j0 | −0.023 | |$^{+0.317}_{-0.397}$| | |$^{+0.748}_{-0.685}$| | 0.545 | |$^{+0.463}_{-0.652}$| | |$^{+1.135}_{-1.025}$| | 1.585 | |$^{+0.497}_{-0.914}$| | |$^{+1.594}_{-1.453}$| |
| s0 | −0.745 | |$^{+0.196}_{-0.284}$| | |$^{+0.564}_{-0.487}$| | 0.118 | |$^{+0.451}_{-1.600}$| | |$^{+3.422}_{-1.921}$| | 1.041 | |$^{+1.183}_{-1.784}$| | |$^{+3.388}_{-3.087}$| |
| M | −19.16 | |$^{+0.07}_{-0.07}$| | |$^{+0.14}_{-0.14}$| | −19.03 | |$^{+0.02}_{-0.02}$| | |$^{+0.05}_{-0.05}$| | −19.17 | |$^{+0.07}_{-0.07}$| | |$^{+0.13}_{-0.13}$| |
| ΔM | −0.054 | |$^{+0.023}_{-0.022}$| | |$^{+0.044}_{-0.045}$| | −0.054 | |$^{+0.022}_{-0.023}$| | |$^{+0.045}_{-0.045}$| | −0.050 | |$^{+0.022}_{-0.022}$| | |$^{+0.044}_{-0.045}$| |
| α | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.130 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| |
| β | 2.624 | |$^{+0.071}_{-0.068}$| | |$^{+0.136}_{-0.140}$| | 2.625 | |$^{+0.065}_{-0.069}$| | |$^{+0.137}_{-0.135}$| | 2.667 | |$^{+0.068}_{-0.069}$| | |$^{+0.137}_{-0.135}$| |
| rd | 149.2 | |$^{+3.7}_{-4.1}$| | |$^{+7.7}_{-7.5}$| | 148.6 | |$^{+3.5}_{-3.8}$| | |$^{+7.5}_{-7.1}$| | 147.2 | |$^{+3.7}_{-4.0}$| | |$^{+7.8}_{-7.5}$| |
68 per cent and 95 per cent confidence level parameter constraints from the MCMC analysis of SN+OHD+BAO data for the fourth-order Taylor, (2,2) Padé and (2,1) rational Chebyshev polynomial approximations of the luminosity distance. H0 values are given in units of km s−1 Mpc−1, while rd values in units of Mpc.
| Parameter . | Taylor . | Padé . | Rational Chebyshev . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . |
| H0 | 65.80 | |$^{+2.09}_{-2.11}$| | |$^{+4.22}_{-4.00}$| | 64.94 | |$^{+2.11}_{-2.02}$| | |$^{+4.12}_{-4.13}$| | 64.95 | |$^{+1.89}_{-1.94}$| | |$^{+3.77}_{-3.77}$| |
| q0 | −0.276 | |$^{+0.043}_{-0.049}$| | |$^{+0.093}_{-0.091}$| | −0.285 | |$^{+0.040}_{-0.046}$| | |$^{+0.087}_{-0.084}$| | −0.278 | |$^{+0.021}_{-0.021}$| | |$^{+0.041}_{-0.042}$| |
| j0 | −0.023 | |$^{+0.317}_{-0.397}$| | |$^{+0.748}_{-0.685}$| | 0.545 | |$^{+0.463}_{-0.652}$| | |$^{+1.135}_{-1.025}$| | 1.585 | |$^{+0.497}_{-0.914}$| | |$^{+1.594}_{-1.453}$| |
| s0 | −0.745 | |$^{+0.196}_{-0.284}$| | |$^{+0.564}_{-0.487}$| | 0.118 | |$^{+0.451}_{-1.600}$| | |$^{+3.422}_{-1.921}$| | 1.041 | |$^{+1.183}_{-1.784}$| | |$^{+3.388}_{-3.087}$| |
| M | −19.16 | |$^{+0.07}_{-0.07}$| | |$^{+0.14}_{-0.14}$| | −19.03 | |$^{+0.02}_{-0.02}$| | |$^{+0.05}_{-0.05}$| | −19.17 | |$^{+0.07}_{-0.07}$| | |$^{+0.13}_{-0.13}$| |
| ΔM | −0.054 | |$^{+0.023}_{-0.022}$| | |$^{+0.044}_{-0.045}$| | −0.054 | |$^{+0.022}_{-0.023}$| | |$^{+0.045}_{-0.045}$| | −0.050 | |$^{+0.022}_{-0.022}$| | |$^{+0.044}_{-0.045}$| |
| α | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.130 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| |
| β | 2.624 | |$^{+0.071}_{-0.068}$| | |$^{+0.136}_{-0.140}$| | 2.625 | |$^{+0.065}_{-0.069}$| | |$^{+0.137}_{-0.135}$| | 2.667 | |$^{+0.068}_{-0.069}$| | |$^{+0.137}_{-0.135}$| |
| rd | 149.2 | |$^{+3.7}_{-4.1}$| | |$^{+7.7}_{-7.5}$| | 148.6 | |$^{+3.5}_{-3.8}$| | |$^{+7.5}_{-7.1}$| | 147.2 | |$^{+3.7}_{-4.0}$| | |$^{+7.8}_{-7.5}$| |
| Parameter . | Taylor . | Padé . | Rational Chebyshev . | ||||||
|---|---|---|---|---|---|---|---|---|---|
| . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . | Mean . | 1σ . | 2σ . |
| H0 | 65.80 | |$^{+2.09}_{-2.11}$| | |$^{+4.22}_{-4.00}$| | 64.94 | |$^{+2.11}_{-2.02}$| | |$^{+4.12}_{-4.13}$| | 64.95 | |$^{+1.89}_{-1.94}$| | |$^{+3.77}_{-3.77}$| |
| q0 | −0.276 | |$^{+0.043}_{-0.049}$| | |$^{+0.093}_{-0.091}$| | −0.285 | |$^{+0.040}_{-0.046}$| | |$^{+0.087}_{-0.084}$| | −0.278 | |$^{+0.021}_{-0.021}$| | |$^{+0.041}_{-0.042}$| |
| j0 | −0.023 | |$^{+0.317}_{-0.397}$| | |$^{+0.748}_{-0.685}$| | 0.545 | |$^{+0.463}_{-0.652}$| | |$^{+1.135}_{-1.025}$| | 1.585 | |$^{+0.497}_{-0.914}$| | |$^{+1.594}_{-1.453}$| |
| s0 | −0.745 | |$^{+0.196}_{-0.284}$| | |$^{+0.564}_{-0.487}$| | 0.118 | |$^{+0.451}_{-1.600}$| | |$^{+3.422}_{-1.921}$| | 1.041 | |$^{+1.183}_{-1.784}$| | |$^{+3.388}_{-3.087}$| |
| M | −19.16 | |$^{+0.07}_{-0.07}$| | |$^{+0.14}_{-0.14}$| | −19.03 | |$^{+0.02}_{-0.02}$| | |$^{+0.05}_{-0.05}$| | −19.17 | |$^{+0.07}_{-0.07}$| | |$^{+0.13}_{-0.13}$| |
| ΔM | −0.054 | |$^{+0.023}_{-0.022}$| | |$^{+0.044}_{-0.045}$| | −0.054 | |$^{+0.022}_{-0.023}$| | |$^{+0.045}_{-0.045}$| | −0.050 | |$^{+0.022}_{-0.022}$| | |$^{+0.044}_{-0.045}$| |
| α | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.127 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| | 0.130 | |$^{+0.006}_{-0.006}$| | |$^{+0.012}_{-0.012}$| |
| β | 2.624 | |$^{+0.071}_{-0.068}$| | |$^{+0.136}_{-0.140}$| | 2.625 | |$^{+0.065}_{-0.069}$| | |$^{+0.137}_{-0.135}$| | 2.667 | |$^{+0.068}_{-0.069}$| | |$^{+0.137}_{-0.135}$| |
| rd | 149.2 | |$^{+3.7}_{-4.1}$| | |$^{+7.7}_{-7.5}$| | 148.6 | |$^{+3.5}_{-3.8}$| | |$^{+7.5}_{-7.1}$| | 147.2 | |$^{+3.7}_{-4.0}$| | |$^{+7.8}_{-7.5}$| |
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