A tale of two double quasars: Hubble constant tension or biases?

For a flat $\Lambda$CDM (standard) cosmology, a small sample of gravitationally lensed quasars with measured time delays has recently provided a value of the Hubble constant $H_0$ in tension with the $Planck$ flat $\Lambda$CDM result. Trying to check if this tension is real or not, we used basic observational constraints for two double quasars of the GLENDAMA sample (SBS 0909+532 and SDSS J1339+1310) to discuss the underlying value of $H_0$ in a standard cosmology. For SBS 0909+532, we were not able to obtain a reliable measurement of $H_0$. However, the current data of SDSS J1339+1310 are consistent with $H_0$ around 67.8 km s$^{-1}$ Mpc$^{-1}$ and $\sigma (H_0)/H_0 \sim$ 10%. Although the formal uncertainty is still large and mainly due to the lack of details on the mass density profile of the main lens galaxy, the central value of $H_0$ coincides with that of the TDCOSMO+SLACS collaboration (using gravitational lens systems) and is within the 1$\sigma$ interval from $Planck$ cosmic microwave background data. After getting these preliminary encouraging results through only one double quasar, we are currently planning to use several GLENDAMA systems to accurately measure the Hubble constant and put constraints on other cosmological parameters.