Probing Dark Energy at Galactic and Cluster Scales
  We investigate dark matter halo properties as a function of a time--varying dark energy equation of state. The dynamics of the collapse of the halo is governed by the form of the quintessence potential, the time evolution of its equation of state, the initial conditions of the field and its homogeneity nature in the highly non--linear regime. These have a direct impact on the turnaround, virialisation and collapse times, altering in consequence the non--linear density contrast and virial radius. We compute halo concentrations using the Eke, Navarro & Steinmetz algorithm, examining two extreme scenarios: first, we assume that the quintessence field does not exhibit fluctuations on cluster scales and below - homogeneous fluid; second, we assume that the field inside the overdensity collapses along with the dark matter - inhomogeneous fluid. The Eke, Navarro & Steinmetz prescription reveals, in general, higher halo concentrations in inhomogeneous dark energy models than in their homogeneous equivalents. Halo concentrations appear to be controlled by both changes in formation epochs of the halo cores as well as by differing virialisation overdensities. We derive physical halo properties in all models and discuss their observational implications. We examine two possible methods for comparing observations with theoretical predictions. The first method works on galaxy cluster scales and consists of fitting the observed X-ray cluster gas density distributions to those predicted for an NFW profile. The second method works on galaxy scales and involves the observational measurement of the so--called central density parameter. 
David F. Mota