This thesis uses theoretical studies, and numerical simulations to provide results of the experimental reach to detect the QCD axion as dark matter in a Non-standard cosmological background. Assuming that the QCD axion constitutes the full CDM abundance of the universe, this thesis elaborates on its potential detection from experimental setups for the mass window of the axion. The set of results that is obtained here are the relic CDM energy density of axions produced by the vacuum realignment mechanism and the CDM energy density of axions produced from the decay of a network of cosmic strings. This thesis provides results regarding the possibility to detect a primordial gravitational wave relic, which is possible within some favorable cosmological scenarios for the background.