What do physicists expect to find or accomplish with gravitational lensing in the next 15 years? Is there a specific type of object, or a concept that they are looking for?
To ask what do physicists expect to accomplish with gravitational lensing is nowadays somewhat like asking what do biologists expect to accomplish with looking at things with microscopes. Gravitational lensing is a well established method used across astronomy and the main challenges the field itself has to tackle are mainly technicalities.
But I will try to give a list of areas where lensing can or certainly will bring breakthroughs.
- Dark matter - The most convincing and quantitative picture of dark matter we have is given by gravitational lensing. Studying dynamical systems such as the bullet cluster or the "not so dark" core of Abel 3827 and subjecting it to lensing analyses are basically the only direct handle we have on dark matter. More detailed surveys will surely allow us to learn more.
- Cosmological parameters - Studying the CMB or the Standard candles is just one way to obtain cosmological parameters. The other way is - wait for it - lensing. Large scale statistics of things such as cosmic shear provide a valuable consistency check of our standard cosmological model. Currently the gravitational lensing statistics indicate cosmological parameters which are not within experimental error with respect to the ones obtained e.g. from the CMB but this is believed to be due to improper error analysis on the lensing side. Gathering more data and strongly confirming a discrepancy with standard cosmology would be a breakthrough.
- Exoplanets - Finding exoplanets by microlensing is nowadays almost a routine task, you just need good enough data and time. In an indirect way, gravitational microlensing is one of the steps in the search for extraterrestrial life.
- ??? - You do not get a Nobel prize for using known tools in a predictable way. One of the keys to scientific progress is unprecedented novelty, so there might be a way gravitational lensing may be useful no one has thought of yet.