A More Accurate and Competitive Estimative of $H_0$ in Intermediate Redshifts

In order to clarify the tension between estimates of the Hubble Constant ($H_0$) from local ($z \ll 1$) and global ($z \gg 1$) measurements, Lima and Cunha (LC) proposed a new method to measure $H_0$ in intermediate redshifts ($z \approx 1$), which were obtained $H_0 = 74.1 \pm 2.2$ km s$^{-1}$Mpc$^{-1}$ ($1 \sigma$), in full agreement to local measurements via Supernovae/Cepheid dataset. However, Holanda \textit{et al.} (2014) affirm that a better understanding of the morphology of galaxy clusters in LC framework is needed to a more robust and accurate determination of $H_0$. Moreover, that kind of sample has been strongly questioned in the literature. In this context, (i) we investigated if the sample of galaxy clusters used by LC has a relevant role in their results, then (ii) we perform a more accurate and competitive determination of $H_0$ in intermediate redshifts, free of unknown systematic uncertainties. First, we found that the exclusion of the sample of galaxy clusters from the determination initially proposed by LC leads to significantly different results. Finally, we performed a new determination in $H_0$, where we obtained $H_0 = 68.00 \pm 2.20$ km s$^{-1}$ Mpc$^{-1}$ ($1 \sigma$) with statistical and systematic errors and $H_0 = 68.71^{+1.37}_{-1.45}$ km s$^{-1}$ Mpc$^{-1}$ ($1 \sigma$) with statistical errors only. Contrary to those obtained by LC, these values are in full harmony with the global measurements via Cosmic Microwave Background (CMB) radiation and to the other recent estimates of $H_0$ in intermediate redshifts.