  We propose a new theory of dark matter based on axion physics and
cosmological phase transitions. We show that theories in which a gauge coupling
increases through a first-order phase transition naturally result in `axion
relic pockets': regions of relic false vacua stabilised by the pressure from a
kinematically trapped, hot axion gas. Axion relic pockets provide a viable and
highly economical theory of dark matter: the macroscopic properties of the
pockets depend only on a single parameter (the phase transition temperature).
We describe the formation, evolution and present-day properties of axion relic
pockets, and outline how their phenomenology is distinct from existing dark
matter paradigms. We briefly discuss how laboratory experiments and
astronomical observations can be used to test the theory, and identify
gamma-ray observations of magnetised, dark-matter-dense environments as
particularly promising.
