Cosmological perturbation theory in Generalized Einstein-Aether models
  We investigate the evolution of cosmological perturbations in models of dark
energy described by a time-like unit normalized vector field specified by a
general function $\mathcal{F}(\mathcal{K})$, so-called Generalized
Einstein-Aether models. First we study the background dynamics of such models
via a designer approach in an attempt to model this theory as dark energy. We
find that only one specific form of this designer approach matches $\Lambda$CDM
at background order and we also obtain a differential equation which
$\mathcal{F}(\mathcal{K})$ must satisfy for general $w$CDM cosmologies. We also
present the equations of state for perturbations in Generalized Einstein-Aether
models, which completely parametrize these models at the level of linear
perturbations. A generic feature of modified gravity models is that they
introduce new degrees of freedom. By fully eliminating these we are able to
express the gauge invariant entropy perturbation and the scalar, vector, and
tensor anisotropic stresses in terms of the perturbed fluid variables and
metric perturbations only. These can then be used to study the evolution of
perturbations in the scalar, vector, and tensor sectors and we use these to
evolve the Newtonian gravitational potentials.
