Decaying dark matter and the tension in $σ_8$

TL;DR

The paper investigates decaying dark matter (DDM) as a mechanism to relieve the $σ_8$ tension between CMB and weak lensing by allowing dark matter to decay into invisible dark radiation with rate $Γ$. It combines linear perturbation theory, N-body simulations, and a non-linear matter power spectrum fitting formula to predict and test DDM against CMB, WL, BAO, and Planck lensing data. The results show that the DDM model exhibits a larger overlap between CMB and WL+BAO posteriors than CDM, suggesting a potential hint for DDM, though current data do not decisively prefer a non-zero decay rate; a joint CMB+WL analysis yields $Γ^{-1} \\ge 97$ Gyr at 95% C.L. (less stringent than the CMB-alone bound of $Γ^{-1} \\ge 140$ Gyr). Overall, the work provides a robust framework and concrete constraints for DDM and indicates that upcoming surveys could decisively test this scenario.

Abstract

We consider decaying dark matter (DDM) as a resolution to the possible tension between cosmic microwave background (CMB) and weak lensing (WL) based determinations of the amplitude of matter fluctuations, $σ_8$. We perform N-body simulations in a model where dark matter decays into dark radiation and develop an accurate fitting formula for the non-linear matter power spectrum, which enables us to test the DDM model by the combined measurements of CMB, WL and the baryon acoustic oscillation (BAO). We employ a Markov chain Monte Carlo analysis to examine the overlap of posterior distributions of the cosmological parameters, comparing CMB alone with WL+BAO. We find an overlap that is significantly larger in the DDM model than in the standard CDM model. This may be hinting at DDM, although current data is not constraining enough to unambiguously favour a non-zero dark matter decay rate $Γ$. From the combined CMB+WL data, we obtain a lower bound $Γ^{-1}\ge 97$ Gyr at 95 % C.L, which is less tight than the constraint from CMB alone.

Figures (5)

• Figure 1: Power spectrum of non-relativistic matter today $(z=0)$, for DDM models with $\Gamma$[Gyr$^{-1}$]=3 (red), 30 (green) and 300 (blue). For reference, the case with the standard CDM is also plotted (magenta).
• Figure 2: Ratio of non-linear matter power spectrum in the DDM model to that in the CDM model. Red, green and blue points with error bars are obtained from N-body simulations with box sizes $L=1250$, $500$ and 200 $h_\emptyset^{-1}$Mpc, respectively. The dashed magenta line is obtained from the linear perturbation calculation in the synchronous gauge by using CAMB. The dotted orange line is obtained by applying our fitting formula in Appendix \ref{['app:fit']}, which exactly overlaps with magenta line on large scales. The solid grey horizontal line indicates unity.
• Figure 3: Constraints on the CDM model. The 1d and 2d posterior distributions for parameters $\omega_{dm}$, $H_0$ and $\sigma_8$ are shown, with the 2d constraints given at 68 % and 95 % C.L. Green, grey, red and blue lines correspond to the data sets WL, CMB, CMB+WL and CMB+WL+BAO+lensing, respectively.
• Figure 4: The same as in Fig. \ref{['fig:CDM']}, but for the DDM model, which has an additional parameter $\Gamma$.
• Figure 5: Enhancement of suppression from linear to non-linear matter power spectrum $\epsilon_{\textrm{non-linear}}(k)/\epsilon_{\rm linear}$ for $\Gamma^{-1}=$31.6, 100, 316 Gyr and $z=$0, 1. Here we adopt the result of N-body simulations with a box size $L=200~h_\emptyset^{-1}$Mpc.