Scale-dependent growth from a transition in dark energy dynamics

We investigate the observational consequences of the quintessence field rolling to and oscillating near a minimum in its potential, if it happens close to the present epoch (z less than or similar to 0: 2). We show that in a class of models, the oscillations lead to a rapid growth of the field fluctuations and the gravitational potential on subhorizon scales. The growth in the gravitational potential occurs on time scales << H-1. This effect is present even when the quintessence parameters are chosen to reproduce an expansion history consistent with observations. For linearized fluctuations, we find that although the gravitational potential power spectrum is enhanced in a scale-dependent manner, the shape of the dark matter/galaxy power spectrum is not significantly affected. We find that the best constraints on such a transition in the quintessence field is provided via the integrated Sachs-Wolfe effect in the CMB-temperature power spectrum. Going beyond the linearized regime, the quintessence field can fragment into large, localized, long-lived excitations (oscillons) with sizes comparable to galaxy clusters; this fragmentation could provide additional observational constraints. Two quoted signatures of modified gravity are a scale-dependent growth of the gravitational potential and a difference between the matter power spectrum inferred from measurements of lensing and galaxy clustering. Here, both effects are achieved by a minimally coupled scalar field in general relativity with a canonical kinetic term. In other words we show that, with some tuning of parameters, scale-dependent growth does not necessarily imply a violation of General Relativity.