Roles of a coherent scalar field on the evolution of cosmic structures

A coherently oscillating scalar field, an axion as an example, is known to behave as a cold dark matter. The arguments were usually made in the Newtonian context. Ratra proved the case in relativistic context using the synchronous gauge. In this Letter we present another proof based on a more suitable gauge condition, the uniform-curvature gauge, which fits the problem. By a proper time averaging the perturbed oscillating scalar field behaves as a cold dark matter on the relevant scales including the superhorizon scale.