Since the gravitational lensing of light was first observed around one hundred years ago, it has became and developed into a standard, mature tool in studying astrophysics and cosmology, for instance, studying the structure of the (lens) galaxy and measuring Hubble constant. In many of these applications, lens reconstruction/modelling is a crucial and necessary middle step.
Meanwhile, following general relativity, gravitational waves should be lensed in the same way as light when they travel near massive objects in space. Despite lensed gravitational waves are not detected yet, it is expected that we will be able to observe such signals within decades, as the gravitational wave detectors keep on advancing. In order to prepare for the big day of first lensed gravitational waves detection, we studied gravitational wave based lens reconstruction in different scenarios, examined different challenges and degeneracies, and looked into various science applications of lensing. We lay out a bit more details below.
Firstly, we probed into gravitational lens reconstruction using lensed gravitational waves observation alone (dark siren). Due to the scale-free nature of various lensing observables, for instance, the magnifications, the dark siren lens reconstruction suffers from ‘similarity transformation degeneracy’, which is a degeneracy between the (angular diameter) distances and the scale of the lens (its Einstein radius). On this end, we introduced new non-degenerate and irreducible set of parameters of the lens system, which accounts for the degenerate and ‘reducible’ parameters. In order to perform various astrophysical studies, such as measuring Hubble constant, we may have to break this degeneracy by obtaining the redshifts of the lens and source through corresponding lensing observation in the electromagnetic band.
Secondly, we examined lens reconstruction using both lensed gravitational waves and electromagnetic signal observation (multi-messenger). While such observation breaks the similarity transformation degeneracy, it still suffers from the well-known mass-sheet degeneracy, which will lead to biased Hubble constant measurement. To break the mass-sheet degeneracy, we will have to obtain non-lensing related information of the lens galaxy, such as its velocity dispersion through spectroscopy measurement.
Lastly, we also discussed the impact of these two degeneracies on various other science applications, such as testing speed of gravity with lensing and associating fast radio bursts with compact binary coalescence. We discovered that, surprisingly, modified gravitational wave propagation test by lensing is not affected by mass-sheet degeneracy.
The paper can be read here: https://arxiv.org/abs/2406.06463. If you have any questions, comments, or interesting ideas, feel free to contact the authors!