Program: GS-2022A-FT-210

RR Lyrae and type II Cepheid variables are sensitive probe for the precision stellar astrophysics and also for the distance scale thanks to their well-defined near-infrared Period-Luminosity relations (PLRs). These population II distance indicators together with the tip of the red giant branch (TRGB) can provide an independent primary calibration of local distance ladder evaluating the ongoing Hubble tension. Since the TRGB-based Hubble constant values fall between population I Cepheid-Supernovae based and the Planck results, TRGB calibration needs to be tested or complemented with population II RR Lyrae or type II Cepheids. We propose JHKs observations of a unique metal-rich bulge globular cluster NGC 6388 which hosts 37 RR Lyrae and the most 10 type II Cepheids in a single cluster. These population II distance indicators in NGC 6388 will enable a direct comparison of their PLRs and a quantification of metallicity dependence when combined with literature data of metal-poor clusters. Homogeneous RR Lyrae and type II Cepheid distances to literature globular clusters will also provide an independent absolute calibration of the TRGB at multiple wavelengths. Our observations will thus provide a critical test of metallicity dependence and the absolute calibration of both RR Lyrae and type II Cepheids and a quantification of systematic uncertainties in the population II distance scale.