ner_tags: O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model B-Model O O B-Model B-Model B-Model O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model B-Model O O O O O O O O O O O O B-Model O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Model O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Model I-Model I-Model O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O
tokens: 2020 ). Detailed information about the data can be found at http://shsuyu.github.io/H0LiCOW/site/h0licow_data.html . The galaxies passively evolving on a time much longer than their age difference can be used as a cosmic chronometer (Jimenez Loeb 2002 ). The age difference between two ensembles of old galaxies at different redshifts gives a direct estimation of the Hubble parameter . We use 31 such measurements of H ( z ) (Simon et al. 2005 ; Stern et al. 2010 ; Moresco et al. 2012 ; Zhang et al. 2014 ; Moresco 2015 ; Moresco et al. 2016 ; Ratsimbazafy et al. 2017 ), which are shown in Figure 1 . For comparison, we also plot the H ( z ) prediction of a typical ΛCDM model with Ω m = 0.3, h = 0.7 and its PAge approximation. Figure 1. Cosmic chronometer data. The red solid line is prediction of ΛCDM model with Ω m = 0.3, h = 0.7, and the green dashed line is its PAge approximation. 4. Results We run Monte Carlo Markov Chain (MCMC) calculations with BAO, SLTD, CC and the their combination (All), respectively. Uniform priors are applied on h ∈ [0.55, 0.85], p age ∈ [0.5, 1.5], η ∈ [−2, 1], and r d h ∈ [0, 1 Gpc]. In addition, following Huang ( 2020 ), we use a cosmic age bound t 0 > 12 Gyr in all cases. The chains and analysis tools are uploaded to https://zenodo.org/record/4065034 to allow future researchers to reproduce our results. We first consider a spatially flat universe whose geometry is fully characterized by h , p age , and η . The marginalized constraints on p age and η , with BAO, SLTD, CC, and their combination are shown in Figure 2 . We find that CC alone does not imply cosmic acceleration, while BAO and SLTD both favor cosmic acceleration at ∼2.5 σ level. With all the data combined together, we obtain a derived posterior of the deceleration parameter q 0 = −0.514 ± 0.116, a ∼4.4 σ detection of cosmic acceleration. For the Hubble constant, we obtain H 0 = 70.7 ± 1.9 km s −1 Mpc −1 that is consistent with both the local distance-ladder measurement and the CMB+ΛCDM result. The derived posterior of the baryon acoustic scale r d = 142.2 ± 2.7 Mpc is consistent with CMB + ΛCDM value 147.18 ± 0.29 Mpc (Aghanim et al. 2020 ). Figure 2. Marginalized constraints on PAge parameters. The inner and outer contours enclose 68% and 95% confidence regions, respectively. The dotted violet contours show the effect of switching on the Ω k freedom for the BAO+SLTD+CC case. Proceeding to the nonflat case with a uniform prior Ω k ∈ [−1, 1], we find that the marginalized constraint on p age and η are not much affected by the addition of Ω k freedom, as Figure 2 visually indicates. The detection of cosmic acceleration remains at a ∼4.1 σ level. Because the spatial curvature has almost no impact around the local universe, we can still compare the posterior of the Hubble constant H 0 = 69.4 ± 1.9 km s −1 Mpc −1 with the distance-ladder measurement, and again find no significant discrepancy. When Ω k is allowed to vary, the data do not favor, however, a