Axion dark matter and the Lattice

First I will review the QCD theta problem and the Peccei-Quinn solution, with its new particle, the axion. I will review the possibility of the axion as dark matter. If PQ symmetry was restored at some point in the hot early Universe, it should be possible to make a definite prediction for the axion mass if it constitutes the Dark Matter. I will describe progress on one issue needed to make this prediction -- the dynamics of axionic string-wall networks and how they produce axions. Then I will discuss the sensitivity of the calculation to the high temperature QCD topological susceptibility. My emphasis is on what temperature range is important, and what level of precision is needed.