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There are a number of approaches to testing General Relativity (GR) on linearscales using parameterized frameworks for modifying cosmological perturbationtheory. It is sometimes assumed that the details of any given parameterizationare unimportant if one uses it as a diagnostic for deviations from GR. In thisbrief report we argue that this is not necessarily so. First we show thatadopting alternative combinations of modifications to the field equationssignificantly changes the constraints that one obtains. In addition, we showthat using a parameterization with insufficient freedom significantly tightensthe apparent theoretical constraints. Fundamentally we argue that it is almostnever appropriate to consider modifications to the perturbed Einstein equationsas being constraints on the effective gravitational constant, for example, inthe same sense that solar system constraints are. The only consistentmodifications are either those that grant near-total freedom, as indecomposition methods, or ones which map directly to a particular part oftheory space.

Ambiguous Tests of General Relativity on Cosmological Scales