Practical tools for third order cosmological perturbations

We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the evolution equations for a perfect fluid, and the Klein-Gordon equation at third order, including scalar, vector and tensor perturbations. In doing so, we also give all second order tensor components and evolution equations in full, exhilarating generality.