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Strongest model-independent bound on the lifetime of Dark Matter

Benjamin Audren, Julien Lesgourgues, Gianpiero Mangano, Pasquale Dario Serpico, Thomas Tram

TL;DR

This paper derives the strongest model-independent cosmological bound on the lifetime of cold dark matter (CDM) by considering decays into relativistic products and their impact on late-time cosmology, particularly the low-$\ell$ region of the CMB. Using two extended models that include the tensor-to-scalar ratio $r$ and curvature $\Omega_k$, and combining Planck, WMAP, WiggleZ, BAO data with or without BICEP2, the authors constrain the decay rate via a full Boltzmann treatment implemented in the CLASS framework. They find a 95% CL lower bound on the CDM lifetime of $\tau_{\text{dcdm}} > 160$ Gyr without BICEP2 and $\tau_{\text{dcdm}} > 200$ Gyr with BICEP2, with degeneracies largely disentangled from $\Omega_k$ and $r$. The bound is robust, model-independent for relativistic decay products, and has implications for particle-physics models (e.g., Majoron scenarios), while future weak-lensing surveys are expected to tighten the constraint further.

Abstract

Dark Matter is essential for structure formation in the late Universe so it must be stable on cosmological time scales. But how stable exactly? Only assuming decays into relativistic particles, we report an otherwise model independent bound on the lifetime of Dark Matter using current cosmological data. Since these decays affect only the low-$\ell$ multipoles of the CMB, the Dark Matter lifetime is expected to correlate with the tensor-to-scalar ratio $r$ as well as curvature $Ω_k$. We consider two models, including $r$ and $r+Ω_k$ respectively, versus data from Planck, WMAP, WiggleZ and Baryon Acoustic Oscillations, with or without the BICEP2 data (if interpreted in terms of primordial gravitational waves). This results in a lower bound on the lifetime of CDM given by 160Gyr (without BICEP2) or 200Gyr (with BICEP2) at 95% confidence level.

Strongest model-independent bound on the lifetime of Dark Matter

TL;DR

This paper derives the strongest model-independent cosmological bound on the lifetime of cold dark matter (CDM) by considering decays into relativistic products and their impact on late-time cosmology, particularly the low- region of the CMB. Using two extended models that include the tensor-to-scalar ratio and curvature , and combining Planck, WMAP, WiggleZ, BAO data with or without BICEP2, the authors constrain the decay rate via a full Boltzmann treatment implemented in the CLASS framework. They find a 95% CL lower bound on the CDM lifetime of Gyr without BICEP2 and Gyr with BICEP2, with degeneracies largely disentangled from and . The bound is robust, model-independent for relativistic decay products, and has implications for particle-physics models (e.g., Majoron scenarios), while future weak-lensing surveys are expected to tighten the constraint further.

Abstract

Dark Matter is essential for structure formation in the late Universe so it must be stable on cosmological time scales. But how stable exactly? Only assuming decays into relativistic particles, we report an otherwise model independent bound on the lifetime of Dark Matter using current cosmological data. Since these decays affect only the low- multipoles of the CMB, the Dark Matter lifetime is expected to correlate with the tensor-to-scalar ratio as well as curvature . We consider two models, including and respectively, versus data from Planck, WMAP, WiggleZ and Baryon Acoustic Oscillations, with or without the BICEP2 data (if interpreted in terms of primordial gravitational waves). This results in a lower bound on the lifetime of CDM given by 160Gyr (without BICEP2) or 200Gyr (with BICEP2) at 95% confidence level.

Paper Structure

This paper contains 15 sections, 13 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Stability and particle physics
  3. Gravitational effects
  4. Previous works
  5. Scope and outline of this paper
  6. Equations and implementation
  7. Background equations
  8. Perturbation equations in synchronous gauge
  9. Perturbation equations in Newtonian gauge
  10. Boltzmann hierarchy for decay radiation
  11. Comparison with data
  12. Observable effects
  13. The data
  14. Results
  15. Conclusions

Figures (5)

  • Figure 1: CMB temperature power spectrum for a variety of models, all with the same parameters $\{100\,\theta_s, \omega_\mathrm{dcdm}^\mathrm{ini}, \omega_\mathrm{b}, \ln(10^{10} A_s), n_s, \tau_\mathrm{reio} \} = \{1.04119, 0.12038, 0.022032, 3.0980, 0.9619, 0.0925\}$ taken from the Planck+WP best fit Ade:2013zuv. For all models except the "Decaying CDM" one, the decay rate $\Gamma_\mathrm{dcdm}$ is set to zero, implying that the "dcdm" species is equivalent to standard cold DM with a present density $\omega_\mathrm{cdm} = \omega_\mathrm{dcdm}^\mathrm{ini} = 0.12038$. The "Decaying CDM" model has $\Gamma_\mathrm{dcdm}=20\,\hbox{km s}^{-1}\hbox{Mpc}^{-1}$, the "Tensors" model has $r=0.2$, and the "Open" ("Closed") models have $\Omega_k = 0.02$ ($-0.2$). The main differences occur at low multiples and comes from either different late ISW contributions or non-zero tensor fluctuations.
  • Figure 2: The single contributions to the CMB temperature spectrum (Sachs-Wolfe, early and late Integrated Sachs-Wolfe, Doppler and polarisation-induced) for a stable model (solid) and a dcdm model (dashed) with $\Gamma_\mathrm{dcdm}=100$ km/s/Mpc. The value of other parameters is set as in Figure \ref{['fig:cltot']}. We see that only the late ISW effect is sensitive to the decay rate (for other contributions, solid and dashed lines are indistinguishable).
  • Figure 3: Matter power spectrum $P(k)$ (computed in the Newtonian gauge) for the same models considered in Figure \ref{['fig:cltot']}. The black curve (Stable CDM) is hidden behind the red one (Tensors).
  • Figure 4: Comparison of the results for $\{ \omega_\mathrm{dcdm+dr}, \Gamma_\mathrm{dcdm}, r \}$ for the $\Lambda$CDM + $\{\Gamma_\mathrm{dcdm}, r \}$ model for the 1-d and 2-d posterior distributions, using the dataset set $A$ (blue contours) and $B$ (yellow/orange contours). The contours represent 68% and 95% confidence levels.
  • Figure 5: For the $\Lambda$CDM + $\{\Gamma_\mathrm{dcdm}, r, \Omega_k \}$ model, comparison of the results for $\{ \omega_\mathrm{dcdm+dr}, \Gamma_\mathrm{dcdm}, r, \Omega_k \}$ using the dataset set $A$ (blue contours) and $B$ (yellow/orange contours), for the 1d and 2d posterior distributions. The contours represent 68% and 95% confidence levels.