Numerical simulation of axion quintessence

Robust, scaled cosmological equations are derived for simulating the evolution of the scalar field, the scale factor, and the Hubble parameter during both expanding and contracting phases of the universe. These scaled equations are applied to both stable (always expanding universe) and unstable axion quintessence (expanding and then collapsing universe). When applied to unstable axion quintessence, these scaled equations allow the simulations presented here to proceed much closer to the singularity at the end of a collapsing universe than any previous simulations.