It has been shown that the axions produced in early universe can account for the cosmological dark matter. Theoretically, axions can decay and their decay rate can be greatly enhanced by stimulated emission of photons. In this article, we present a theoretical framework to describe the decay of the cosmological axion dark matter. We show that, for a certain parameter space of axion mass ma and the axion–photon coupling constant gaΥΥ, the axion decay would be significantly triggered so that no axion dark matter remains. For the popular benchmark models of the cosmological axion dark matter ma∼10−5 eV, current observational constraints of the axion–photon coupling constant can ensure that axions are stable enough to be the cosmological dark matter. Copyright © 2023 The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.