[Paper Review] Implications of the $S_8$ tension for decaying dark matter with warm decay products

Guillermo Franco Abellán, Riccardo Murgia+2 more|arXiv (Cornell University)|Aug 21, 2020

Cosmology and Gravitation Theories13 citations

TL;DR

This paper proposes a two-body decaying dark matter (ΛDDM) model where cold dark matter decays into a massive warm dark matter particle and a massless dark radiation component, suppressing structure formation via free-streaming. With a lifetime of ~55 Gyr and energy transfer fraction ε ≈ 0.7%, the model resolves the S8 tension by reducing σ8, while simultaneously fitting CMB, BAO, SNIa, and growth factor data, offering a viable alternative to standard ΛCDM.

ABSTRACT

Recent weak lensing surveys have revealed that the direct measurement of the parameter combination $S_8\equiv\sigma_8(\Omega_m/0.3)^{0.5}$ -- where $\sigma_8$ is a measure of the amplitude of matter fluctuations on 8 $h^{-1}$Mpc scales -- is $\sim3\sigma$ discrepant with the value reconstructed from cosmic microwave background (CMB) data assuming the $\Lambda$CDM model. In this article, we show that it is possible to resolve the tension if dark matter (DM) decays with a lifetime of $\Gamma^{-1} \simeq 55 \ ext{Gyrs}$ into one massless and one massive product, and transfers a fraction $\varepsilon\simeq 0.7 \ \%$ of its rest mass energy to the massless component. The velocity-kick received by the massive daughter leads to a suppression of gravitational clustering below its free-streaming length, thereby reducing the $\sigma_8$ value as compared to that inferred from the standard $\Lambda$CDM model, in a similar fashion to massive neutrino and standard warm DM. Contrarily to the latter scenarios, the time-dependence of the power suppression and the free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB, baryon acoustic oscillation, growth factor and un-calibrated supernova Ia data. We briefly discuss implications for DM model building, galactic small-scale structure problems and the recent Xenon-1T excess. Future experiments measuring the growth factor to high accuracy at $0\lesssim z\lesssim1$ can further test this scenario.

Motivation & Objective

• To resolve the S8 tension—3σ discrepancy between CMB-inferred and weak lensing-measured σ8(Ωm/0.3)⁰.⁵—within the ΛCDM framework.
• To explore whether two-body decaying dark matter with warm decay products can suppress small-scale power without conflicting with existing cosmological data.
• To test whether such a model can simultaneously accommodate CMB lensing, BAO, uncalibrated SNIa, and growth factor measurements.
• To assess the model’s viability in addressing small-scale structure problems and the Xenon-1T excess.

Proposed method

• Introduces a two-body decay model (ΛDDM) where dark matter decays into one massive warm dark matter (WDM) particle and one massless dark radiation (DR) component.
• Uses a novel fluid approximation for the WDM species, reducing the phase-space distribution to three multipoles on sub-Hubble scales, enabling efficient numerical computation.
• Implements the full perturbation equations for DCDM, WDM, and DR in the CLASS numerical code, including linear cosmological perturbations.
• Performs a Monte Carlo Markov Chain (MCMC) analysis using MontePython-v3, fitting to Planck high-ℓ and low-ℓ CMB data, BAO, SNIa (Pantheon), and S8 measurements.
• Models the S8 likelihood as a split-normal function based on KIDS1000+BOSS+2dfLenS data, with S8 = 0.766⁺⁰.⁰²₀₋₀.⁰¹⁴.
• Compares the model to standard ΛCDM and massive neutrino (νΛCDM) scenarios using the QDMAP tension metric and Bayesian evidence.

Experimental results

Research questions

• RQ1 Can a two-body decaying dark matter model with warm decay products resolve the S8 tension while remaining consistent with CMB, BAO, and SNIa data?
• RQ2 How does the time-dependent suppression of the matter power spectrum in this decay model differ from standard massive neutrino or WDM scenarios?
• RQ3 What are the required decay parameters (lifetime and energy transfer fraction) to reconcile S8 with CMB data without violating other cosmological constraints?
• RQ4 Can this model simultaneously explain the Xenon-1T excess and alleviate small-scale structure problems in ΛCDM?
• RQ5 How sensitive are the results to the choice of prior on the decay parameters (log vs. linear)?

Key findings

• The model resolves the S8 tension with a dark matter decay lifetime of approximately 55 Gyr and an energy transfer fraction of ε ≈ 0.7% to the massless component.
• The warm daughter particle induces a time-dependent suppression of the matter power spectrum below its free-streaming scale, reducing σ8 in a way analogous to massive neutrinos or standard WDM.
• The model successfully fits Planck CMB, BAO, uncalibrated SNIa, and S8 data simultaneously, unlike previous 2-body decay models that failed under combined BAO and CMB lensing constraints.
• The results are robust to prior choice: the 1D and 2D posteriors for ε and Γ are largely unaffected by changing the lower bound of the prior on ε from 10⁻⁴ to 10⁻⁶.
• The model cannot resolve the Hubble tension, as confirmed by exclusion from combined BAO, SNIa, and Planck data in prior studies.
• The Bayesian evidence favors the ΛDDM model over ΛCDM when including S8 data, indicating improved fit to the full dataset.