Lattice formulation of axion inflation. Application to preheating

We present a lattice formulation of an interaction {\phi\over\Lambda} F\tilde Fbetween an axion and some U(1)gauge sector with the following properties: it reproduces the continuum theory up to \mathcal{O}(dx_\mu^2)corrections, it preserves exact gauge invariance and shift symmetry on the lattice, and it is suitable for self-consistent expansion of the Universe. The lattice equations of motion can no longer be solved by explicit...