Testing the quasi-static approximation in $f(R)$ gravity simulations

Understand

Numerical simulations in modified gravity have commonly been performed under the quasi-static approximation -- that is, by neglecting the effect of time derivatives in the equation of motion of the scalar field that governs the fifth force in a given modified gravity theory.

• To test the validity of this approximation, we analyse the case of $f(R)$ gravity beyond this quasi-static limit, by considering effects, if any, these terms have in the matter and velocity divergence cosmic fields.
• To this end, we use the adaptive mesh refinement code ECOSMOG to study three variants ($|f_{R}|= 10^{-4}[$F4$], 10^{-5}[$F5$]$ and $10^{-6}[$F6$]$) of the Hu-Sawicki $f(R)$ gravity model, each of which refers to a different magnitude for the scalar field that generates the fifth force.
• We find that for F4 and F5, which show stronger deviations from standard gravity, a low-resolution simulation is enough to conclude that time derivatives make a negligible contribution to the matter distribution.