Parametrized post-Friedmann framework for modified gravity

The expansion history H and the metric ratio g define completely super-horizon scalar metric fluctuations for adiabatic perturbations.

“The expansion history H and the metric ratio g define completely super-horizon scalar metric fluctuations for adiabatic perturbations.”

For modified gravity models affecting cosmic evolution after matter-radiation equality, the three functions governing metric, density and velocity relations plus the usual transfer functions specify fully the linear observables of the model.

“For MG models affecting cosmic evolution after matter radiation equality, these 3 functions governing the relations for the metric, the density and the velocity, plus the usual transfer functions specify fully the linear observables of the model.”

The exact form of the function expressing the super-horizon relationship between the metric and density is rarely important for observable quantities such as galaxy redshift surveys and gravitational lensing.

“As noted there, the exact form of is rarely important for observable quantities. That is the case, for example, for the galaxy redshift surveys and gravitational lensing.”

Hu and Sawicki found that the PPF function rescales the effective Newton constant and that the quasi-static transition happens near the horizon scale.

“Last, they find that is the function that rescales the effective Newton constant and the quasi-static transition happens near the horizon scale.”

The PPF formalism of Hu and Sawicki (2007b) was proposed with a prescription to derive the nonlinear matter power spectrum in modified gravity theories that should in principle capture the screening mechanism.

“Third, the PPF formalism of Hu and Sawicki (2007b) was proposed with a prescription on how to derive the nonlinear matter power spectrum in modified gravity theories that should in principle capture the screening mechanism as well.”

Hu and Sawicki (2007b) constructed a PPF formalism for linear perturbations in modified gravity models that joins the super-horizon regime and the sub-horizon quasi-static regime.

“They construct a PPF formalism for linear perturbations in MG models that joins the super-horizon regime and the sub-horizon quasi-static regime.”