Testing the quasi-static approximation inf(R) gravity simulations

Abstract

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 (|fR| = 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. The F6 model shows a larger deviation from the quasi-static approximation, but one that diminishes when re-simulated at higher-resolution. We therefore come to the conclusion that the quasi-static approximation is valid for the most practical applications in f (R) cosmologies.

Testing gravity using cosmic voids

“…Cai et al 2014), and will not be repeated here. In this paper, we are interested in the formation of large-scale structures on scales substantially below the horizon, and the time variation of f R is small in the models we will consider (Bose, Hellwing & Li 2015). Therefore, we will work with the quasi-static approximation by neglecting the time derivatives of f R in all field equations.…”

Weak lensing by voids in modified lensing potentials

“…[84,85] for discussions about the quasi-static limit, and Refs. [86,87] for work beyond this in N-body simulations). One may speculate that the terms which are neglected in the quasi-static limit are actually responsible for keeping the fifth force real for all density values when they are present.…”

Exploring the liminality: properties of haloes and subhaloes in borderlinef(R) gravity

“…On these scales, we can apply the quasi-static approximation by neglecting the time derivatives of f R in all field equations (see e.g. Bose, Hellwing & Li 2015, for tests which show that this approximation works well for the model studied here). Then equation (3) simplifies to…”