Cosmic Axions
  The current cosmological constraints on a dark matter axion are reviewed. We describe the basic mechanisms by which axions are created in the early universe, both in the standard thermal scenario in which axion strings form and in inflationary models. In the thermal scenario, the dominant process for axion production is through the radiative decay of an axion string network, which implies a dark matter axion of mass m_a ~ 100 microeV with specified large uncertainties. An inflationary phase does not affect this string bound if the reheat temperature is high T_reh > f_a or, conversely, for T_reh < f_a, if the Hubble parameter during inflation is large H_1 > f_a; in both cases, strings form and we return to the standard picture with a m_a ~ 100 microeV dark matter axion. Inflationary models with f_a > H_1 > T_reh face strong CMBR constraints and require `anthropic misalignment' fine-tuning in order to produce a dark matter axion; in this case, some inflation models are essentially incompatible with a detectable axion, while others can be engineered to allow a dark matter axion anywhere in a huge mass range below m_a < 1 meV. We endeavour to clarify the sometimes confusing and contradictory literature on axion cosmology. 
E. P. S. Shellard and R. A. Battye (University of Cambridge)