The combinatorial and disordered universe

Cosmology represents our window on the most fundamental principles in physics, being the energies of the processes in the primordial universe 10 order of magnitude higher than the ones at the LHC and tantalizingly close to the Planck scale. In this talk, I will stress how ideas coming from different fields such as theoretical particle physics and disordered systems can shed light on such principles and their consequences. In particular, on one side they can lead to model independent constraints on the physics at such energies, and on the other they suggest how a change of mathematical language can favour a deeper understanding of connection between the high energy physics and our low energy knowledge.