# Revisiting Vainshtein Screening for fast N-body simulations

**Authors:** Guilherme Brando, Kazuya Koyama, Hans A. Winther  
**arXiv:** [2303.09549](https://arxiv.org/abs/2303.09549)  
**Date:** 2023-03-16  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.09549v1/

## Key points

- Large Scale Structure (LSS) of the Universe contains valuable information about the evolution of linear and Gaussian perturbations into complex structures observed in the sky.
- N-body simulations are used to compute matter power spectrum accurately in non-linear regimes by solving geodesic and Poisson equations following a given theory of gravity.
- Data from surveys such as DESI, Euclid, and Rubin observatory's LSST open up possibilities for probing dark energy.
- The authors revisit a method proposed by R. Scoccimarro to incorporate Vainshtein screening in N-body simulations.
- This approach is extended to cover a subset of Horndeski theories that evade constraints on gravitational wave speed set by GW170817.
- The procedure involves computing an effective gravitational coupling that is time and scale dependent ($G_{\rm eff}\left(k,z\right)$), which incorporates fifth-force screening.
- To test their approach's validity in nonlinear regimes, they implement it in a COmoving Lagrangian Approximation (COLA) N-body code and run simulations for two gravity models with full N-body simulation outputs available: nDGP and Cubic Galileon.
- They validate combining COLA with this implementation of Vainshtein mechanism with full N-body simulations for predicting boost function - ratio between modified gravity nonlinear matter power spectrum and its General Relativity counterpart.
- This quantity is essential for building emulators in beyond-$\Lambda$CDM models.
- Their method has an agreement below $2\%$ for scales down to $k \approx 3h/$Mpc concerning full N-body simulations.
- The authors' work provides an efficient way to study LSS cosmology beyond GR while reducing computational costs significantly.

## Summary

The Large Scale Structure (LSS) of the Universe contains a wealth of information about how linear and Gaussian perturbations evolved into the complex structure we observe in the sky. N-body simulations are used to accurately compute the matter power spectrum in the deeply non-linear regime by solving geodesic and Poisson equations following a given theory of gravity. Data from surveys such as DESI, Euclid, and Rubin observatory's LSST open up the possibility of probing dark energy. In this paper, the authors revisit a method proposed by R. Scoccimarro to incorporate Vainshtein screening in N-body simulations. This approach is extended to cover a subset of Horndeski theories that evade constraints on gravitational wave speed set by GW170817. The procedure involves computing an effective gravitational coupling that is time and scale dependent ($G_{\rm eff}\left(k,z\right)$), which incorporates fifth-force screening. This reduces computational time and complexity compared to solving full equations for scalar fields inside N-body codes. To test their approach's validity in nonlinear regimes, they implement it in a COmoving Lagrangian Approximation (COLA) N-body code and run simulations for two gravity models with full N-body simulation outputs available: nDGP and Cubic Galileon. They validate combining COLA with this implementation of Vainshtein mechanism with full N-body simulations for predicting boost function - ratio between modified gravity nonlinear matter power spectrum and its General Relativity counterpart. This quantity is essential for building emulators in beyond-$\Lambda$CDM models. Their method has an agreement below $2\%$ for scales down to $k \approx 3h/$Mpc concerning full N-body simulations. The authors' work provides an efficient way to study LSS cosmology beyond GR while reducing computational costs significantly.