We introduce $\texttt{ Hi-COLA}$, a code designed to run fast, approximate $\textit{ N}$-body simulations of non-linear structure formation in reduced Horndeski gravity. Given an input Lagrangian, $\texttt{ Hi-COLA}$ dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. Hence $\texttt{ Hi-COLA}$ is a general, adaptable, and useful tool that allows the mildly non-linear regime of many Horndeski theories to be investigated for the first time, at low computational cost. In this work, we first describe the screening approximations and simulation setup of $\texttt{ Hi-COLA}$ for theories with Vainshtein screening. We validate the code against traditional $\textit{ N}$-body simulations for cubic Galileon gravity, finding $2.5\%$ agreement up to $k_{ \rm max}=1.2~h/{ \rm Mpc}$. To demonstrate the flexibility of $\texttt{ Hi-COLA}$, we additionally run the first simulations of an extended shift-symmetric gravity theory. We use the consistency and modularity of $\texttt{ Hi-COLA}$ to dissect how the modified background, linear growth, and screened fifth force all contribute to departures from $\Lambda$CDM in the non-linear matter power spectrum. $\texttt{ Hi-COLA}$ can be found at https://github.com/Hi-COLACode/Hi-COLA .
Categories: astro-ph.CO