Demonstration of the ULA mass and redshift dependent regime change in the Hubble rate. In the pink regime, ULAs contribute to the Hubble rate e in a manner similar to dark matter; in the blue region, ULAs contribute to the Hubble rate in a dark energy-like fashion. The orange shaded region shows the eRASS1 cluster redshift range, while the gray shaded region shows the redshift range of lensed galaxies from the DES, HSC, and KiDS data, described in Sect. 3.2. Above a ULA mass of m_a ∼ 10^−31.5 eV, ULAs should be modeled as dark matter in the Hubble rate, resulting in correct distance measurements during the parameter inference. For ULAs with masses below m_a ∼ 10^−31.5 eV, the distance measurements are affected by the regime change via the Hubble rate, where ULAs are treated as dark energy.