Currently, there is an intriguing discord between measurements of the expansion rate of the Universe based on early- and late-Universe probes. It appears as a discrepancy in the value of the Hubble constant, H₀ , as derived from measurements of the anisotropy of the cosmic microwave background and as measured from a series of distance indicators in the local Universe.

Currently, that tension is between 4σ and 6σ (Verde+2019, 2013). This could point to a serious measurement error (which has not been identified despite several years of improvements), or imply a need to revise our understanding of the cosmos and its fundamental physical laws. Cosmology controls the thermal history of the Universe and its evolution from the Big Bang to the origin of life. The purpose of the present proposal is to raise the accuracy of the astronomical distance ladder by specifically tackling uncertainties and systematics affecting stellar standard candles, in order to cast light on the origin of the tension and at the same time to better understand the underlying stellar physics.

To achieve this challenging goal we will rely on the diverse expertise of the proposing team and on the access to a variety of datasets (spanning a wide range of techniques, instruments and wavelength ranges). In this context, the project will develop through complementary approaches (relativistic astrometry, asteroseismology, theory of stellar evolution, stellar pulsation, stellar populations, photometry and time series analysis) and will be organized in a number of relevant steps aimed at understanding and quantifying the H 0 tension as arising from the distance ladder side. We will plan a number of meetings, conveniently scheduled such as to take the best advantage of the upcoming Gaia Early Data Release 3 and Data Release 3.