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A fresh look at linear cosmological constraints on a decaying dark matter component

Vivian Poulin, Pasquale D. Serpico, Julien Lesgourgues

TL;DR

This paper develops a Boltzmann-hierarchy treatment for a cosmology where a fraction $f_{ m dcdm}$ of dark matter decays into invisible dark radiation with rate $\Gamma_{ m dcdm}$, providing corrected background and perturbation equations and examining the resulting imprints on the CMB and matter power spectrum. Using Planck CMB data (and later including low-redshift probes), the authors map constraints on $(f_{ m dcdm}, \Gamma_{ m dcdm})$ across three lifetime regimes, finding $f_{ m dcdm}\Gamma_{ m dcdm} < 6.3\times10^{-3}$ Gyr$^{-1}$ for long lifetimes, and $f_{ m dcdm}\Gamma_{ m dcdm}$ tightening to about $5.9\times10^{-3}$ Gyr$^{-1}$ with full Planck TTTEEE data; when including consistent low-z data the bound becomes $5.8\times10^{-3}$ Gyr$^{-1}$, or $\tau_{ m dcdm}/f_{ m dcdm}>170$ Gyr. A key result is that degeneracies with neutrino mass are broken by large-scale structure and lensing data, strengthening the robustness of the bounds. The analysis also discusses non-linear modeling limitations for applying CFHT-like data and notes that while decaying DM can modestly alleviate some CMB-low-z tensions, it does not fully resolve them, implying either systematics or a need for alternative new physics. Overall, the work provides a rigorous, data-driven assessment of how a decaying DM component impacts cosmology and what current observations imply for such models, with implications for exotic DM candidates like primordial black holes.

Abstract

We consider a cosmological model in which a fraction $f$ of the Dark Matter (DM) is allowed to decay in an invisible relativistic component, and compute the resulting constraints on both the decay width (or inverse lifetime) $Γ$ and $f$ from purely gravitational arguments. We report a full derivation of the Boltzmann hierarchy, correcting a mistake in previous literature, and compute the impact of the decay --as a function of the lifetime-- on the CMB and matter power spectra. From CMB only, we obtain that no more than 3.8 % of the DM could have decayed in the time between recombination and today (all bounds quoted at 95 % CL). We also comment on the important application of this bound to the case where primordial black holes constitute DM, a scenario notoriously difficult to constrain. For lifetimes longer than the age of the Universe, the bounds can be cast as $fΓ< 6.3\times10^{-3}$ Gyr$^{-1}$. For the first time, we also checked that degeneracies with massive neutrinos are broken when information from the large scale structure is used. Even secondary effects like CMB lensing suffice to this purpose. Decaying DM models have been invoked to solve a possible tension between low redshift astronomical measurements of $σ_8$ and $Ω_{\rm m}$ and the ones inferred by Planck. We reassess this claim finding that with the most recent BAO, HST and $σ_8$ data extracted from the CFHT survey, the tension is only slightly reduced despite the two additional free parameters, loosening the bound to $fΓ< 15.9\times10^{-3}$ Gyr$^{-1}$. The bound however improves to $fΓ< 5.9\times10^{-3}$ Gyr$^{-1}$ if only data consistent with the CMB are included. This highlights the importance of establishing whether the tension is due to real physical effects or unaccounted systematics, for settling the reach of achievable constraints on decaying DM.

A fresh look at linear cosmological constraints on a decaying dark matter component

TL;DR

This paper develops a Boltzmann-hierarchy treatment for a cosmology where a fraction of dark matter decays into invisible dark radiation with rate , providing corrected background and perturbation equations and examining the resulting imprints on the CMB and matter power spectrum. Using Planck CMB data (and later including low-redshift probes), the authors map constraints on across three lifetime regimes, finding Gyr for long lifetimes, and tightening to about Gyr with full Planck TTTEEE data; when including consistent low-z data the bound becomes Gyr, or Gyr. A key result is that degeneracies with neutrino mass are broken by large-scale structure and lensing data, strengthening the robustness of the bounds. The analysis also discusses non-linear modeling limitations for applying CFHT-like data and notes that while decaying DM can modestly alleviate some CMB-low-z tensions, it does not fully resolve them, implying either systematics or a need for alternative new physics. Overall, the work provides a rigorous, data-driven assessment of how a decaying DM component impacts cosmology and what current observations imply for such models, with implications for exotic DM candidates like primordial black holes.

Abstract

We consider a cosmological model in which a fraction of the Dark Matter (DM) is allowed to decay in an invisible relativistic component, and compute the resulting constraints on both the decay width (or inverse lifetime) and from purely gravitational arguments. We report a full derivation of the Boltzmann hierarchy, correcting a mistake in previous literature, and compute the impact of the decay --as a function of the lifetime-- on the CMB and matter power spectra. From CMB only, we obtain that no more than 3.8 % of the DM could have decayed in the time between recombination and today (all bounds quoted at 95 % CL). We also comment on the important application of this bound to the case where primordial black holes constitute DM, a scenario notoriously difficult to constrain. For lifetimes longer than the age of the Universe, the bounds can be cast as Gyr. For the first time, we also checked that degeneracies with massive neutrinos are broken when information from the large scale structure is used. Even secondary effects like CMB lensing suffice to this purpose. Decaying DM models have been invoked to solve a possible tension between low redshift astronomical measurements of and and the ones inferred by Planck. We reassess this claim finding that with the most recent BAO, HST and data extracted from the CFHT survey, the tension is only slightly reduced despite the two additional free parameters, loosening the bound to Gyr. The bound however improves to Gyr if only data consistent with the CMB are included. This highlights the importance of establishing whether the tension is due to real physical effects or unaccounted systematics, for settling the reach of achievable constraints on decaying DM.

Paper Structure

This paper contains 15 sections, 20 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Boltzmann equations for the decaying Dark Matter
  3. Background equations
  4. Perturbation equations in gauge invariant variables
  5. Cosmological effects of a decaying Dark Matter fraction
  6. Impact of Dark Matter decay on the CMB
  7. Impact of the decaying Dark Matter on the matter power spectrum
  8. Potential degeneracy with the neutrino mass
  9. Application of the decaying dark matter model
  10. Constraints from the CMB power spectra only
  11. Adding low redshift astronomical data
  12. Linear vs Non-linear matter power spectrum
  13. The low-redshift data discrepancies
  14. The strongest bounds on the decaying Dark Matter fraction and lifetime from mutually consistent data
  15. Conclusions

Figures (11)

  • Figure 1: Comparison of the lensed TT (top) and EE (bottom) power spectra for several decaying DM lifetimes and a fixed abundance $f_{\rm dcdm} = 0.2$. Boxes show the (binned) cosmic variance uncertainty.
  • Figure 2: Top panel $-$ Comparison of the matter power spectrum for several decaying DM lifetimes and a fixed abundance $f_{\rm dcdm} = 0.2$. Bottom panel $-$ Evolution of the background densities for two different models of DM with $f_{\rm dcdm} = 0.4$, compared to the standard $\Lambda$CDM model. The vertical lines indicates the value of the matter-radiation and matter-$\Lambda$ equalities in each model. Note that matter-radiation equality happens at the same redshift in the standard $\Lambda$CDM and the DCDM model with $\Gamma_{\rm dcdm}=10^3$ Gyr$^{-1}$, therefore lines are superimposed.
  • Figure 3: Comparison of the lensed TT (top), EE (middle) and matter (bottom) power spectra for several decaying DM lifetimes and several neutrino masses. The value $f_{\rm dcdm}=0.027$ (resp. 0.08) has been chosen in order to compensate the effect of $M_\nu=0.3$ eV (resp. 0.9 eV) and obtain the same total dark matter density today, $\omega_{\textrm{m}}$. The inverse of $\Gamma_{\rm dcdm}$ has been adjusted to the time of the neutrino non-relativistic transition. Boxes show the (binned) cosmic variance uncertainty.
  • Figure 4: Constraints on the decaying dark matter fraction $f_{\rm dcdm}$ as a function of the lifetime $\Gamma_{\rm dcdm}$ in the long-lived and intermediate regime. All datasets also include CMB low-$\ell$ data from each spectrum and the lensing reconstruction. Blue (red) lines and contours refer to the case without (with) high-$\ell$ polarization data. Inner and outer coloured regions denote $1\,\sigma$ and $2~\sigma$ contours, respectively.
  • Figure 5: Constraints as in Fig. \ref{['fig:ConstraintsCMBOnly']}, but for the short-lived dcdm regime. We also show how the distribution of the initial cdm density evolves when the decay rate and dcdm fraction increase.
  • ...and 6 more figures