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

¹ Instituto de Física de Cantabria (CSIC-UC) Avda. Los Castros s/n 39005 Santander, Spain
² Center for Astrophysics | Harvard & Smithsonian 60 Garden St. Cambridge MA 02138, USA
³ School of Earth and Space Exploration, Arizona State University Tempe AZ 85287-6004, USA

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 3 January 2025
Accepted: 16 November 2025

Abstract

Gravitational lensing by galaxy clusters can create extreme magnification (μ > 1000) near the cluster caustics, thereby enabling detections of individual luminous stars in high-redshift background galaxies. These stars can include nonexplosive standard candles such as Cepheid variables, carbon stars in the asymptotic giant branch (AGB), and stars at the tip of the red giant branch (TRGB) out to z ≲ 1. 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. The feature comes from the great abundance of red giant branch stars just below the luminosity of the TRGB. This feature is still present even when microlenses smooth out the sharp jump in the luminosity function at the TRGB. The apparent magnitude at which the knee is observed depends on the value of the Hubble constant, H₀, and the surface mass density of microlenses, Σ_* (with a weak dependence on the macromodel magnification). Therefore, a precise measurement of Σ_* is needed in order to use the TRGB knee as a distance indicator. As a bonus, strongly lensed stars detected in deep exposures also provide a robust method of mapping small dark matter substructures, detections of which will cluster around the critical curves of small-scale dark matter halos. The sensitivity of the TRGB knee to Σ_* also allows novel avenues to constrain the abundance of compact dark matter such as primordial black holes. Cepheids will also be detectable, but because microlenses modify their apparent luminosity by unknown magnification factors, the main value of Cepheids will be improving cluster lens models.