Motivated by the cosmological importance of coherent (classical), scalar-field oscillations in the context of the invisible axion and the new inflationary-universe scenario, we analyze, in general, the classical evolution of a scalar field in an isotropic and homogeneous cosmology. For a scalar potential of the form $V\left(\phi \right)=a{\phi }^n$, the energy density of the scalar-field oscillations decreases as $R^{-\frac{6n}{\mathrm{}(n+2\mathrm{})\mathrm{}}}$ when the oscillations are rapid compared to the expansion rate ($R=\mathrm{cosmic}\mathrm{scale}\mathrm{factor}$). We also investigate the effect of higher-order terms in the potential perturbatively, and analyze the decay of the coherent field oscillations due to quantum particle creation.

• Received 8 June 1983

DOI:https://doi.org/10.1103/PhysRevD.28.1243