In this talk we will introduce CosmoLattice, a modern code for simulating the non-linear dynamics of interactive scalar-gauge theories in an expanding universe. As a demonstration of its power we will solve three very different problems of early Universe cosmology: i) the generation and use of gravitational waves as a probe of particle couplings, ii) the dynamics of non-minimally coupled scalar fields in the Jordan frame, and iii) the non-linear dynamics of helical gauge field production during the last efoldings of axion-inflation