Cosmological Structure Formation in Decaying Dark Matter Models

TL;DR

This paper investigates a decaying dark matter model where dark matter particles decay into massive daughters, affecting small-scale structure formation, and provides empirical tools to compare with observations and constrain model parameters.

Contribution

It introduces self-consistent N-body simulations and empirical fitting functions for DDM, enabling accurate modeling of its impact on structure formation and constraints from observational data.

Findings

DDM can suppress small-scale structures more effectively than WDM.

Empirical fitting functions accurately model DDM effects on the mass function and power spectrum.

Constraints on DDM parameters are derived from Lyman-$eta$ observations and halo model comparisons.

Abstract

The standard cold dark matter (CDM) model predicts too many and too dense small structures. We consider an alternative model that the dark matter undergoes two-body decays with cosmological lifetime $\tau$ into only one type of massive daughters with non-relativistic recoil velocity $V_k$. This decaying dark matter model (DDM) can suppress the structure formation below its free-streaming scale at time scale comparable to $\tau$. Comparing with warm dark matter (WDM), DDM can better reduce the small structures while being consistent with high redshfit observations. We study the cosmological structure formation in DDM by performing self-consistent N-body simulations and point out that cosmological simulations are necessary to understand the DDM structures especially on non-linear scales. We propose empirical fitting functions for the DDM suppression of the mass function and the mass-concentration relation, which depend on the decay parameters lifetime $\tau$ and recoil velocity $V_k$, and redshift. The fitting functions lead to accurate reconstruction of the the non-linear power transfer function of DDM to CDM in the framework of halo model. Using these results, we set constraints on the DDM parameter space by demanding that DDM does not induce larger suppression than the Lyman-$\alpha$ constrained WDM models. We further generalize and constrain the DDM models to initial conditions with non-trivial mother fractions and show that the halo model predictions are still valid after considering a global decayed fraction. Finally, we point out that the DDM is unlikely to resolve the disagreement on cluster numbers between the Planck primary CMB prediction and the Sunyaev-Zeldovich (SZ) effect number count for $\tau \sim H_{0}^{-1}$.