Extending the cosmic distance ladder two orders of magnitude with strongly lensed Cepheids, carbon AGB, and RGB stars

Gravitational lensing by galaxy clusters can create extreme magnification near the cluster caustics, thereby enabling detection of individual luminous stars in high-redshift background galaxies. Those stars can include non-explosive standard candles such as Cepheid variables, carbon stars in the asymptotic giant branch, and stars at the tip of the red-giant branch out to $z\lesssim1$. A large number of such detections, combined with modeling of the magnification affecting these stars (including microlensing), opens the door to extending the distance range of these standard candles by two orders of magnitude, thereby providing a check on the distances derived from supernovae. Practical measurement of a distance modulus depends on measuring the apparent magnitude of a ``knee feature'' in the lensed luminosity function due to the great abundance of red-giant-branch stars just below the luminosity of the tip of the red-giant branch. As a bonus, strongly lensed stars detected in deep exposures also provide a robust method of mapping small dark-matter substructures, detections of which also cluster around the critical curves of small-scale dark matter halos.