Classical pulsating stars such as Cepheid and RR Lyrae are sensitive probes for both the stellar astrophysics and the cosmic distance scale. Cepheid variables play a vital role in calibrating extragalactic distance ladder to estimate the local value of the Hubble constant – present expansion rate of the Universe. The current Hubble constant measurement in the late evolutionary Universe based on the Cepheid-Supernovae distance ladder is significantly larger than the Planck mission results from the early Universe. This tension hints at possible new physics beyond the standard cosmological model and warrants a rigorous investigation of potential systematic uncertainties in Cepheid-based distance ladder. The proposed project will use state-of-the-art stellar pulsation models to compute and exploit an unprecedently fine grid of Cepheid and RR Lyrae models. These models together with future Gaia data-releases will be used to calibrate theoretical and empirical Period-Luminosity relations for Cepheid and RR Lyrae, and quantify residual systematic effects in the first-rung of the distance ladder and evaluate the significance of the Hubble tension problem. The project will employ modern computational methods for multiwavelength comparison between predicted and observed pulsation properties and full-amplitude light and velocity variations to constrain the mass-luminosity relations and helium to metal enrichment ratio followed by Cepheid and RR Lyrae stars with sub-percent precision for the first-time. These investigations will also discriminate and quantify the effects of poorly understood non-standard phenomena such as mass-loss, rotation or convective overshooting on input stellar physics to the pulsation codes, and thus imply strong constraints for the stellar evolutionary models. This project is of multidisciplinary nature with a strong transfer of knowledge between the applicant and the host researcher, and in line with the EU strategic plan for research and innovation.