Mainly all cosmological observations consist of light in different wavelengths (except, for example, binary black hole collisions, which produce gravitational waves exclusively). In Newtonian physics, light propagation and gravitation are separate phenomena where one does not affect the other. In Einstein's general relativity, however, light produces gravitational field (mostly negligible unless the energy density of light is quite high), and gravitational field affects light propagation. For example, light rays passing near a massive object are bent due to the gravitational field produced by the object. Therefore, just like an ordinary lens, massive galaxy clusters (gravitational lens) in between us (observer) and distant galaxies (source) distort, magnify and change the brightness of source images. A part of this project is to improve upon the mathematical framework that describes gravitational lensing, especially approximations in the weak-field limit, without applying ad-hoc assumptions.

In cosmology, finding the distance to a luminous object requires a model. The standard model of cosmology in which the expanding universe is the same everywhere (homogeneous) and in every direction (isotropic) at large scales (~100 million lightyears) is quite successful so far. For example, it is incredible that the measurement of the local expansion rate of the universe (Hubble constant) from two different datasets at extremely different length scales even gives a close answer. However, in terms of statistics, this expansion rate differs by three standard deviations. Perhaps one of the problems is that the universe, at small scales, is not homogeneous; there is so much empty space between galaxies, stars, and planets. Therefore, an inhomogeneous model of the universe that mimics the standard model at large scales and considers inhomogeneities on small scales would accurately describe our universe and be consistent with datasets at various length scales. (If one chooses a highly inhomogeneous model, for example, the accelerated expansion of the universe, a discovery that was awarded a Nobel prize, could just be apparent. However, this model must be consistent with all other datasets finding the same parameters.) A part of this project is to develop inhomogeneous models.

The project as a whole is to develop inhomogeneous models of the universe, improve upon the theory of gravitational lensing and apply the latter to the former.

Einstein once said that the most incomprehensible thing about the universe is that it is comprehensible. Cosmology has entered the era of precise observations, with many large-scale projects lined up in the near future. Understanding the theory of gravitational lensing, for example, gives a new level of admiration to the beautiful images captured by the James Webb telescope in which galaxies appear stretched or almost ring-like.