# COLA with massive neutrinos

## TL;DR

This paper develops a computationally efficient method to incorporate massive neutrinos into COLA simulations, accurately modeling their scale-dependent effects on structure growth in cosmology.

## Contribution

It introduces a way to compute scale-dependent growth factors for modified gravity and neutrinos in Lagrangian perturbation theory within COLA, matching full N-body results.

## Key findings

- Achieves percent-level accuracy in matter power spectra up to k≈1 h/Mpc.
- Successfully integrates massive neutrinos into COLA with minimal computational cost.
- Demonstrates compatibility with existing scale-dependent growth models.

## Abstract

The effect of massive neutrinos on the growth of cold dark matter perturbations acts as a scale-dependent Newton's constant and leads to scale-dependent growth factors just as we often find in models of gravity beyond General Relativity. We show how to compute growth factors for $\Lambda$CDM and general modified gravity cosmologies combined with massive neutrinos in Lagrangian perturbation theory for use in COLA and extensions thereof. We implement this together with the grid-based massive neutrino method of Brandbyge and Hannestad in $\texttt{MG-PICOLA}$ and compare COLA simulations to full $\it N$-body simulations of $\Lambda$CDM and $f(R)$ gravity with massive neutrinos. Our implementation is computationally cheap if the underlying cosmology already has scale-dependent growth factors and it is shown to be able to produce results that match $\it N$-body to percent level accuracy for both the total and CDM matter power-spectra up to $k\lesssim 1 h/$Mpc.