Coherent scalar-field oscillations in an expanding universe

Abstract

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 $V(\ensuremath{\varphi})=a{\ensuremath{\varphi}}^{n}$, the energy density of the scalar-field oscillations decreases as ${R}^{\ensuremath{-}\frac{6n}{(n+2)}}$ 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.