Parameterized beyond-Einstein growth

A single parameter, the gravitational growth index γ, succeeds in characterizing the growth of density perturbations in the linear regime separately from the effects of the cosmic expansion. The parameter is restricted to a very narrow range for models of dark energy obeying the laws of general relativity but can take on distinctly different values in models of beyond-Einstein gravity. Motivated by the parameterized post-Newtonian (PPN) formalism for testing gravity, we analytically derive and extend the gravitational growth index, or minimal modified gravity, approach to parameterizing beyond-Einstein cosmology. The analytic formalism demonstrates how to apply the growth index parameter to early dark energy, time-varying gravity, DGP braneworld gravity, and some scalar–tensor gravity.