  Parameterized frameworks for modified gravity are potentially useful tools
for model-independent tests of General Relativity on cosmological scales. The
toy model of an Einstein-de Sitter (EdS) universe provides a safe testbed in
which to improve our understanding of their behaviour. We implement a
mathematically consistent parameterization at the level of the field equations,
and use this to calculate the evolution of perturbations in an EdS scenario.
Our parameterization explicitly allows for new scalar degrees of freedom, and
we compare this to theories in which the only degrees of freedom come from the
metric and ordinary matter. The impact on the Integrated Sachs-Wolfe effect and
canonically-conserved superhorizon perturbations is considered.
