How to optimally parametrize deviations from General Relativity in the evolution of cosmological perturbations

The next generation of weak lensing surveys will trace the growth of large scale perturbations through a sequence of epochs, offering an opportunity to test General Relativity (GR) on cosmological scales. We review in detail the parametrization used in MGCAMB to describe the modified growth expected in alternative theories of gravity and generalized dark energy models. We highlight its advantages and examine several theoretical aspects. In particular, we show that the same set of equations can be consistently used on super-horizon and sub-horizon linear scales. We also emphasize the sensitivity of data to scale-dependent features in the growth pattern, and propose using Principal Component Analysis to converge on a practical set of parameters which is most likely to detect departures from GR. The connection with other parametrizations is also discussed.