This is an informal, yet hopefully entertaining talk by a non-expert. After a short (and undoubtedly
incomplete) discussion of some basic puzzles confronting present-day cosmology, I recall the Friedmann Equations for the evolution of a homogeneous, isotropic universe and then proceed to describe the quantum-mechanical state of the universe shortly after inflation. This leads me to speculate about a possible mechanism, based on the chiral magnetic effect, for the growth of intergalactic magnetic fields in the early universe. This mechanism is a fourdimensional cousin of the quantum Hall effect. I then discuss ideas how to unify models of Dark Matter and Dark Energy into a single theory, which, in addition, might shed light on the origin of the matter-antimatter asymmetry of the universe.
