# Comprehensive Study of Neutrino-Dark Matter Mixed Damping

## TL;DR

This paper systematically analyzes mixed damping caused by neutrino-dark matter interactions, deriving analytical approximations and emphasizing the importance of precise numerical treatment for understanding cosmological perturbation suppression.

## Contribution

It establishes the relevant parameter space for mixed damping and provides an analytical approximation for dark matter perturbation evolution in this regime.

## Key findings

- Mixed damping significantly suppresses cosmological perturbations under certain conditions.
- Proper initial conditions and high-order moments are crucial for accurate numerical modeling.
- The study clarifies the physical processes behind damping effects in neutrino-dark matter interactions.

## Abstract

Mixed damping is a physical effect that occurs when a heavy species is coupled to a relativistic fluid which is itself free streaming. As a cross-case between collisional damping and free-streaming, it is crucial in the context of neutrino-dark matter interactions. In this work, we establish the parameter space relevant for mixed damping, and we derive an analytical approximation for the evolution of dark matter perturbations in the mixed damping regime to illustrate the physical processes responsible for the suppression of cosmological perturbations. Although extended Boltzmann codes implementing neutrino-dark matter scattering terms automatically include mixed damping, this effect has not been systematically studied. In order to obtain reliable numerical results, it is mandatory to reconsider several aspects of neutrino-dark matter interactions, such as the initial conditions, the ultra-relativistic fluid approximation and high order multiple moments in the neutrino distribution. Such a precise treatment ensures the correct assessment of the relevance of mixed damping in neutrino-dark matter interactions.