Simulating the quartic Galileon gravity model on adaptively refined meshes

TL;DR

This paper presents a novel numerical algorithm implemented in an adapted N-body code to simulate the quartic Galileon gravity model, revealing the Vainshtein mechanism's effectiveness and its limitations in suppressing scalar field variations.

Contribution

We developed and tested a new numerical method for simulating the quartic Galileon model, enabling the first self-consistent N-body simulations of this modified gravity theory.

Findings

Vainshtein mechanism effectively suppresses scalar field variations

Time variation of Newtonian constant cannot be fully suppressed

Gravity weakens in high-density regions at late times

Abstract

We develop a numerical algorithm to solve the high-order nonlinear derivative-coupling equation associated with the quartic Galileon model, and implement it in a modified version of the RAMSES N-body code to study the effect of the Galileon field on the large-scale matter clustering. The algorithm is tested for several matter field configurations with different symmetries, and works very well. This enables us to perform the first simulations for a quartic Galileon model which provides a good fit to the cosmic microwave background (CMB) anisotropy, supernovae and baryonic acoustic oscillations (BAO) data. Our result shows that the Vainshtein mechanism in this model is very efficient in suppressing the spatial variations of the scalar field. However, the time variation of the effective Newtonian constant caused by the curvature coupling of the Galileon field cannot be suppressed by the Vainshtein mechanism. This leads to a significant weakening of the strength of gravity in high-density regions at late times, and therefore a weaker matter clustering on small scales. We also find that without the Vainshtein mechanism the model would have behaved in a completely different way, which shows the crucial role played by nonlinearities in modified gravity theories and the importance of performing self-consistent N-body simulations for these theories.