A nonuniform dark energy fluid: Perturbation equations

We propose that galactic dark matter can be described by a nonuniform dark energy fluid. The underlying field is a decaying vector field, which might corresponds to a photon-like but massive particle of 4 degrees of dynamical freedom. We propose a very general Lagrangian for this vector field. The model includes a continuous spectrum of plausible gravity theories, for example, quintessence, f(R), Einstein-Aether, MOND, TeVeS, BSTV, V-Lambda theories, and the inflaton scalar field as special cases. We study in detail a special class of models with a fixed norm of the timelike vector field in the physical metric, which includes a nonlinear K-4 term and a Ricci scalar term. We derive the Einstein equations in the perturbed form, which are needed for simulating structure growth in an FRW universe to test such theories. A special case of the model V-Lambda shows promise of resembling the Lambda CDM cosmology. We show that the vector field has the effect of a nonuniform dark fluid, which resembles dark matter in galaxies and dark energy in the late universe.