# Fully relativistic treatment of decaying cold dark matter in $N$-body simulations

## TL;DR

This paper develops a fully relativistic $N$-body simulation framework for decaying cold dark matter, demonstrating that Newtonian simulations are sufficient at small scales when parameters are properly adjusted.

## Contribution

It introduces a self-consistent relativistic $N$-body simulation method for decaying dark matter models, bridging linear theory and non-linear evolution.

## Key findings

- Simulation results match linear Einstein-Boltzmann codes at large scales.
- Newtonian $N$-body simulations are adequate at small scales with proper modifications.
- General relativity effects can be neglected at small scales in these models.

## Abstract

We present $N$-body simulations in which either all, or a fraction of, the cold dark matter decays non-relativistically to a relativistic, non-interacting dark radiation component. All effects from radiation and general relativity are self-consistently included at the level of linear perturbation theory, and our simulation results therefore match those from linear Einstein-Boltzmann codes such as CLASS in the appropriate large-scale limit. We also find that standard, Newtonian $N$-body simulations adequately describe the non-linear evolution at smaller scales ($k \gtrsim 0.1 \, h/{\mathrm{Mpc}}$) in this type of model, provided that the mass of the decaying component is modified correctly, and that the background evolution is correctly treated. That is, for studies of small scales, effects from general relativity and radiation can be safely neglected.