Distinguishing wormholes via Einstein rings and global curvature

Abstract

In this work, we investigate the gravitational lensing properties of a static Ellis-Bronnikov wormhole embedded in a curved Friedmann-Lemaître-Robertson-Walker (FLRW) universe. By employing curvature-dependent cosmological distances, we derive the corresponding weak-field lens equation and demonstrate that the wormhole Einstein ring radius follows a characteristic cubic scaling with cosmological distances, in sharp contrast to the square-root behavior found for Schwarzschild black holes. This distinct scaling leads to a qualitatively different redshift evolution of the lensing signal, providing a model-independent geometric diagnostic to discriminate between wormhole and black hole lensing scenarios. Numerical analysis reveals that the interplay between the local wormhole geometry and the FLRW background produces an asymmetric response to spatial curvature that inverts at intermediate redshifts, exhibiting a non-negligible sensitivity even under tight modern constraints such as those from DESI 2024. We also find that Ellis-Bronnikov wormholes are substantially less efficient gravitational lenses than Schwarzschild black holes of comparable physical scale, implying that microarcsecond-scale Einstein rings require macroscopic throat radii. These results suggest that, should a population of cosmological wormholes exist, their lensing signatures could provide a sensitive, complementary probe of both exotic spacetime topology and the global geometry of the Universe.