This area of our research is concerned with addressing the following unresolved puzzles of the Cosmological Standard Model: The origin of dark matter and dark energy (the embarrassing fact that 20 per cent of the matter and 75 per cent of the energy of the Universe are in a form that is presently unknown); The problem of matter-antimatter asymmetry (the problem of why there is a tiny excess of matter over antimatter in the Universe, at a level of one part in a billion, without which there would be no stars, planets or life); The question of the size, age, flatness and smoothness of the Universe (the question of why the Universe is much larger and older than the Planck size and time, and why it has a globally flat geometry with a very smooth cosmic microwave background radiation). The approaches we develop are based on ideas of Inflationary Cosmology and Leptogenesis which are related to the latest ideas of physics Beyond the Standard Model (see above).