If you look at the original paper Section I. Modeling deviations from GR, their equation 1 gives the metric they've decided to use for this paper. This equation

If you look at the original paper Section I. Modeling deviations from GR, their equation 1 gives the metric they've decided to use for this paper. This equation contains 2 "Newtonian potentials describing temporal and spatial perturbations to the metric." In other words, the paper is about testing Newtonian parameters. They refer to this paper as the source of their equation 1: Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges by Ma and Bertschinger. http://arxiv.org/abs/astro-ph/9506072 http://arxiv.org/abs/astro-ph/9506072 Again, it's about Newtonian parameters.