The 'tip' of the red giant branch as a distance indicator: Results from evolutionary models

New theoretical evaluations of the red giant branch tip (TRGB) luminosity, obtained by adopting the most recent physical inputs in the computing of canonical stellar models, are presented. Theoretical relations for the variation of the TRGB bolometric and I magnitude with the metallicity are provided, together with a comparison of the distance scale based on these relations the RR Lyrae distance scale presented in Cassisi & Saiaris, and the Cepheid distance scale adopted by Lee, Freedman & Madore. This comparison - performed by adopting a sample of Galactic globular clusters and a sample of resolved galaxies - discloses a satisfactory agreement between theory and observations at the level of 0.1 mag. This occurrence can be regarded as evidence for consistency between the theoretical red giant horizontal branch stellar models and independent Cepheid observations, and allows us to safely use the provided TRGB luminosity relations as an alternative primary distance indicator for galaxies in which the stellar component has been resolved.