# Real Scalar Dark Matter: Relativistic Treatment

## TL;DR

This paper presents a fully relativistic analysis of a real scalar dark matter candidate, exploring its thermalization, freeze-out regimes, and observational constraints, highlighting its potential to be warm or cold dark matter.

## Contribution

It introduces a relativistic treatment of scalar dark matter evolution, including a new Bose-Einstein analog of the Gelmini-Gondolo formula and comprehensive parameter space analysis.

## Key findings

- Dark matter can be warm or cold depending on parameters.
- Relativistic effects significantly influence freeze-out and thermalization.
- New formula for thermal averaged cross section derived.

## Abstract

A stable real scalar provides one of the simplest possibilities to account for dark matter. We consider the regime where its coupling to the Standard Model fields is negligibly small. Due to self-coupling, the scalar field can reach thermal or at least kinetic equilibrium, in which case the system is characterized by its temperature and effective chemical potential. We perform a fully relativistic analysis of dark matter evolution, thermalization conditions and different freeze-out regimes, including the chemical potential effects. To this end, we derive a relativistic Bose-Einstein analog of the Gelmini-Gondolo formula for a thermal averaged cross section. Finally, we perform a comprehensive parameter space analysis to determine regions consistent with observational constraints. Dark matter can be both warm and cold in this model.