In this contribution, we give a brief overview for the current state-of-the-art of axion dark matter simulations in the post-inflationary scenario, which allow for a precise prediction of the axion dark matter mass.
The study of post-inflationary axions poses severe computational challenges due to the presence of large hierarchies in the network of topological defects, i.e. strings and domain walls, which inevitably forms if the Peccei-Quinn (PQ) symmetry is broken after inflation. This leads to strong limitations for the potential reach of such simulations, and predictions for the axion dark matter mass usually involve extrapolations over several orders of magnitude in the string tension.
We comment on different approaches to increase the dynamical range of the simulations, with a focus on Adaptive Mesh Refinement (AMR) and Effective Models that allow us to simulate networks at higher string tensions.
As an outlook, we briefly present some details of our current comprehensive study on the radiation emitted by isolated global axion string loops.