# Matter Power Spectrum of Light Freeze-in Dark Matter: With or without Self-Interaction

## TL;DR

This paper investigates how light freeze-in dark matter affects the matter power spectrum, considering both scenarios with negligible and strong self-interactions, and finds that self-scattering can protect small-scale structures from free-streaming suppression.

## Contribution

It introduces a numerical analysis of self-scattering effects on the matter power spectrum in light freeze-in dark matter models, highlighting the importance of decoupling time.

## Key findings

- A 24 keV freeze-in dark matter is excluded by current WDM bounds.
- Strong self-scattering can protect the power spectrum from free-streaming suppression.
- Self-scattering decoupling time is a key parameter in structure formation.

## Abstract

We study the free-streaming effect in a light freeze-in dark matter model. Naturally in the dark sector one can find dark matter related coupling, and such coupling may induce dark matter self-scattering. In case that such scattering is subdominant, the dark matter partition function is not thermal but determined by the freeze-in process, yet its high momentum side is generally also Boltzmann suppressed. We show that the matter power spectrum is very similar to a warm dark matter one in shape. When matched to the current WDM bound, a $24$~keV freeze-in dark matter is ruled out at $2\sigma$ confidence level. In case that the dark matter self-scattering is strong and decouples at a very late time, by a new numerical calculation we show that the early stage Brownian motion indeed protects the power spectrum against free-streaming suppression. However, such an effect cannot be characterized by a free-streaming length alone; we find that the self-scattering decoupling time is another necessary parameter. The currently interested dark matter self-interaction cross section $\sim\text{cm}^2/\text{g}$ is just marginal for such protection to be effective.