Cosmic jerk, snap and beyond

We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and generalized Chaplygin gas energy-momentum tensors. In each case it leads to a constraint on the scalars thus giving rise to a test of general relativity. We also discuss a formulation of the Friedmann equation as unparametrized geodesic motion and its connection with the Lagrangian treatment of perfect fluids coupled to gravity