Dynamical and gravitational instability of an oscillating-field dark energy and dark matter

Coherent oscillations of a scalar field can mimic the behavior of a perfect fluid with an equation-of-state parameter determined by the properties of the potential, possibly driving accelerated expansion in the early Universe (inflation) and/or in the Universe today (dark energy) or behaving as dark matter. We consider the growth of inhomogeneities in such a field, mapping the problem to that of two coupled anharmonic oscillators. We provide a simple physical argument that oscillating fields with a negative equation-of-state parameter possess a large-scale dynamical instability to growth of inhomogeneities. This instability renders these models unsuitable for explaining cosmic acceleration. We then consider the gravitational instability of oscillating fields in potentials that are close to, but not precisely, harmonic. We use these results to show that if axions make up the dark matter, then the small-scale cutoff in the matter power spectrum is around 10-15M+.