Formulation and constraints on decaying dark matter with finite mass daughter particles

TL;DR

This paper develops a comprehensive model for decaying dark matter with arbitrary daughter particle masses, deriving Boltzmann equations and constraining model parameters using cosmological observations.

Contribution

It introduces a complete set of Boltzmann equations for decaying dark matter with arbitrary daughter masses and derives observational constraints on decay lifetime and mass ratios.

Findings

Lower bound on dark matter lifetime: >30 Gyr from CMB data.

Mass ratio constraint: daughter particles are nearly as massive as mother particles.

Free-streaming effects impose tight bounds on mass ratios for short lifetimes.

Abstract

Decaying dark matter cosmological models have been proposed to remedy the overproduction problem at small scales in the standard cold dark matter paradigm. We consider a decaying dark matter model in which one CDM mother particle decays into two daughter particles, with arbitrary masses. A complete set of Boltzmann equations of dark matter particles is derived which is necessary to calculate the evolutions of their energy densities and their density perturbations. By comparing the expansion history of the universe in this model and the free-streaming scale of daughter particles with astronomical observational data, we give constraints on the lifetime of the mother particle, $\Gamma^{-1}$, and the mass ratio between the daughter and the mother particles $m_{\rm D}/m_{\rm M}$. From the distance to the last scattering surface of the cosmic microwave background, we obtain $\Gamma^{-1}>$ 30 Gyr in the massless limit of daughter particles and, on the other hand, we obtain $m_{\rm D} >$ 0.97$m_{\rm M}$ in the limit $\Gamma^{-1}\to 0$. The free-streaming constraint tightens the bound on the mass ratio as $(\Gamma^{-1}/10^{-2}{\rm Gyr}) \lesssim ((1-m_{\rm D1}/m_{\rm M})/10^{-2})^{-3/2}$ for $\Gamma^{-1} < H^{-1}(z=3)$.