The Hubble constant is a key cosmological parameter that sets the present-day expansion rate as well as the age, size, and critical density of the Universe. Intriguingly, there is currently a tension in the measurements of its value in the standard flat ΛCDM model – observations of the Cosmic Microwave Background with the Planck satellite lead to a value of the Hubble constant that is lower than the measurements from the local Cepheids-supernovae distance ladder and strong gravitational lensing. Precise and accurate Hubble constant measurements from independent probes, including water masers, are necessary to assess the significance of this tension and the possible need of new physics beyond the current standard cosmological model. We present the progress toward an accurate Hubble constant determination.

Using high accuracy distance estimates, we study the three-dimensional distribution of galaxies in five galaxy groups at a distance less than 5 Mpc from the Milky Way. Due to proximity of these groups our sample of galaxies is nearly complete down to extremely small dwarf galaxies with absolute magnitudes MB = -12. We find that the average number-density profile of the groups shows a steep power-law decline dn/dV ∼ R-3 at distances R=(100–500) kpc consistent with predictions of the standard cosmological model. We also find that there is no indication of a truncation or a cutoff in the density at the expected virial radius: the density profile extends at least to 1.5 Mpc. Vast majority of galaxies within 1.5 Mpc radius around group centres are gas-rich star-forming galaxies. Early-type galaxies are found only in the central ∼ 300 kpc region. Lack of dwarf spheroidal and dwarf elliptical galaxies in the field and in the outskirts of large groups is a clear indication that these galaxies experienced morphological transformation when they came close to the central region of forming galaxy group.

A new non-parametric method based on Gaussian Processes (GP) was proposed recently to measure the Hubble constant H0. The freedom in this approach comes in the chosen covariance function, which determines how smooth the process is and how nearby points are correlated. We perform coverage tests with a thousand mock samples within the ΛCDM model in order to determine what covariance function provides the least biased results. The function Matérn(5/2) is the best with sligthly higher errors than other covariance functions, although much more stable when compared to standard parametric analyses.

We perform an all-sky search for classical (type I) Cepheids that are members of Galactic Open Clusters. Our approach is multi-dimensional, using all available spatial and kinematic parameters. The quantification of errors is crucial for this analysis, so care is taken to find adequate and realistic representations of parameter uncertainties. The data employed in the calculation are taken from published catalogues and the literature, supplemented by specific radial-velocity observations. Our work in progress is outlined here, and issues related to the inhomogeneity of cluster radii in the literature are discussed in some detail.