Title: The HII Galaxy Hubble Diagram Strongly Favors $R_{\rm h}=ct$ over $Λ$CDM Show Chinese title

Title: HII星系哈勃图强烈支持$R_{\rm h}=ct$而不是$Λ$CDM

Abstract: We continue to build support for the proposal to use HII galaxies (HIIGx) and giant extragalactic HII regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. Using a sample of 25 high-redshift HIIGx, 107 local HIIGx, and 24 GEHR, we confirm that the correlation between the emission-line luminosity and ionized-gas velocity dispersion is a viable luminosity indicator, and use it to test and compare the standard model $\Lambda$CDM and the $R_{\rm h}=ct$ Universe by optimizing the parameters in each cosmology using a maximization of the likelihood function. For the flat $\Lambda$CDM model, the best fit is obtained with $\Omega_{\rm m}= 0.40_{-0.09}^{+0.09}$. However, statistical tools, such as the Akaike (AIC), Kullback (KIC) and Bayes (BIC) Information Criteria favor $R_{\rm h}=ct$ over the standard model with a likelihood of $\approx 94.8\%-98.8\%$ versus only $\approx 1.2\%-5.2\%$. For $w$CDM (the version of $\Lambda$CDM with a dark-energy equation of state $w_{\rm de}\equiv p_{\rm de}/\rho_{\rm de}$ rather than $w_{\rm de}=w_{\Lambda}=-1$), a statistically acceptable fit is realized with $\Omega_{\rm m}=0.22_{-0.14}^{+0.16}$ and $w_{\rm de}= -0.51_{-0.25}^{+0.15}$ which, however, are not fully consistent with their concordance values. In this case, $w$CDM has two more free parameters than $R_{\rm h}=ct$, and is penalized more heavily by these criteria. We find that $R_{\rm h}=ct$ is strongly favored over $w$CDM with a likelihood of $\approx 92.9\%-99.6\%$ versus only $0.4\%-7.1\%$. The current HIIGx sample is already large enough for the BIC to rule out $\Lambda$CDM/$w$CDM in favor of $R_{\rm h}=ct$ at a confidence level approaching $3\sigma$. Show Chinese abstract

Abstract: 我们继续支持使用HII星系（HIIGx）和巨大河外HII区（GEHR）作为标准烛光来构建红移超出目前Ia型超新星范围的哈勃图。 使用25个高红移HIIGx、107个本地HIIGx和24个GEHR的样本，我们确认发射线光度与电离气体速度弥散之间的相关性是一个可行的光度指示器，并用它来测试和比较标准模型$\Lambda$CDM 和$R_{\rm h}=ct$宇宙，通过在每种宇宙学中最大化似然函数来优化参数。 对于平坦的$\Lambda$CDM 模型，最佳拟合是通过$\Omega_{\rm m}= 0.40_{-0.09}^{+0.09}$得到的。 然而，统计工具，如Akaike（AIC）、Kullback（KIC）和Bayes（BIC）信息准则更倾向于$R_{\rm h}=ct$而不是标准模型，其似然为$\approx 94.8\%-98.8\%$而仅为$\approx 1.2\%-5.2\%$。 对于$w$CDM（$\Lambda$CDM 的版本，具有暗能量状态方程$w_{\rm de}\equiv p_{\rm de}/\rho_{\rm de}$而不是$w_{\rm de}=w_{\Lambda}=-1$），通过$\Omega_{\rm m}=0.22_{-0.14}^{+0.16}$和$w_{\rm de}= -0.51_{-0.25}^{+0.15}$实现了统计上可接受的拟合，然而它们与各自的协调值并不完全一致。 在这种情况下，$w$CDM比$R_{\rm h}=ct$多两个自由参数，并且这些标准对其惩罚更严重。我们发现$R_{\rm h}=ct$被强烈偏好于$w$CDM，其似然为$\approx 92.9\%-99.6\%$，而仅为$0.4\%-7.1\%$。 当前的HIIGx样本已经足够大，足以使BIC在接近$3\sigma$的置信水平下排除$\Lambda$CDM/$w$CDM，而支持$R_{\rm h}=ct$。