Gauging the inner mass power spectrum of early-type galaxies

Galaxies are gravitationally bound systems in the Cosmos, mostly made of stars, interstellar dust, gas and dark matter. The dark matter alone constitutes 85% of the total mass of the universe, but it does not interact with electromagnetic radiation, such as light. So, we can not ‘see' this dark matter. However, it does interact gravitationally, and one of the best ways to detect dark matter is therefore via 'gravitational lensing'. Matter that is concentrated in galaxies or in clusters of galaxies, situated between an observer (like us on earth) and a distant source (like another galaxy in the background), can act similar to a 'lens', and is able to gravitationally deflect the trajectory of light that travels from the source to the observer. This phenomenon is one of the most profound predictions of Einstein's general theory of relativity. The research presented in this thesis attempts to quantify the distribution of mass in massive elliptical galaxies using gravitational lensing, especially the presence of this mysterious dark matter on small sub-galactic scales, as well as other contributions that play their role as 'gravitational lens', but which are difficult or almost impossible to detect otherwise. This thesis reports the development of novel statistical techniques to quantify these mass distributions, and also computational frameworks for simulating artificial images of 'lensed' galaxies. Moreover, theoretical research has been connected and applied to real astronomical observations, along with other applications such as artificial intelligence to find gravitational lenses and creating mock lenses using cosmological simulations