On the Magnitude of Dark Energy Voids and Overdensities

We investigate the clustering of dark energy within matter overdensities and voids. In particular, we derive an analytical expression for the dark energy density perturbations, which is valid in the linear, quasi-linear, and fully nonlinear regimes of structure formation. We also investigate the possibility of detecting such dark energy clustering through the integrated Sachs-Wolfe effect. In the case of uncoupled quintessence models, if the mass of the field is of order the Hubble scale today or smaller, dark energy fluctuations are always small compared to the matter density contrast. Even when the matter perturbations enter the nonlinear regime, the dark energy perturbations remain linear. We find that virialized clusters and voids correspond to local overdensities in dark energy, with δ_ϕ/(1 + w) ∼ O(10⁻⁵) for voids, δ_ϕ/(1 + w) ∼ O(10⁻⁴) for supervoids, and δ_ϕ/(1 + w) ∼ O(10⁻⁵) for a typical virialized cluster. If voids with radii of 100-300 Mpc exist within the visible universe, then δ_ϕ may be as large as 10⁻³(1 + w) . Linear overdensities of matter and superclusters generally correspond to local voids in dark energy; for a typical supercluster, δ_ϕ/(1 + w) ∼ O(− 10⁻⁵) . The approach taken in this work could be straightforwardly extended to study the clustering of more general dark energy models.