The Cepheid Distance Scale: from the Local Gaia Calibration to Distant Galaxies

Cepheids are pulsating variable stars which play a key role as primary distance indicators thanks to the empirical relation between their pulsation period and intrinsic luminosity, the period-luminosity relation. This law is used to calibrate the brightness of type-Ia supernovae in nearby galaxies, which is in turn used to measure the distance to galaxies in the Hubble flow. This provides an estimate of the current expansion rate of the Universe, known as the Hubble constant (H₀). In recent years, a significant tension of at least 4\(\sigma\) has arisen between the early universe measurement of H₀ from the Planck satellite, assuming a \(\Lambda\)CDM model, and the late universe direct measurements based on Cepheid distances. The persistence of this tension would imply new physics beyond the standard model of cosmology: it is therefore critical to improve the period-luminosity calibration with precise and reliable Cepheid distance measurements. The Gaia Collaboration recently published trigonometric parallaxes for 1.7 billion stars, allowing for a remarkable improvement in the precision of the distance scale. However, Cepheid parallaxes suffer from calibration issues due to their variability and important brightness. In this thesis, I present an alternative method for calibrating the period-luminosity relation using Cepheid companions and host open clusters, which are not subject to these issues. By adopting these close and unbiased companion stars to determine the distance to Cepheids, I calibrate the period-luminosity relation in the Milky Way and re-evaluate the local value of the Hubble constant. Finally, I study the relation between Cepheid magnitudes and their metal abundance by comparing the Cepheids of the Milky Way and those of the Magellanic Clouds. I conclude that metal-rich Cepheids are brighter than metal-poor ones, with a stronger effect in near-infrared than in optical. This effect may impact the measurement of the Hubble constant and will have to be taken into account more precisely in the future, to better constrain the calibration of the extragalactic distance scale.