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Alleviating the $H_0$ and $σ_8$ anomalies with a decaying dark matter model

Kanhaiya L. Pandey, Tanvi Karwal, Subinoy Das

TL;DR

The paper investigates a decaying dark matter model where DM decays into dark radiation at a rate Γ = α_dr H to jointly address the Hubble tension and the $S_8$ tension. By altering the early-universe expansion and reducing late-time matter density, the model increases $H_0$ and lowers $S_8$, with α_dr governing the effect. Across data combinations, Planck-only favors tiny α_dr (≤0.003), while Planck+R18 can push α_dr to ~0.005±0.003, moderately alleviating both tensions; however, incorporating intermediate-redshift data (JLA+BAO) weakens the improvement and keeps tensions at ~2.5σ for $H_0$ and ~1.5σ for $S_8$, indicating the model cannot fully resolve the anomalies with current data.

Abstract

The Hubble tension between the $Λ$CDM-model-dependent prediction of the current expansion rate $H_0$ using Planck data and direct, model-independent measurements in the local universe from the SH0ES collaboration disagree at $>3.5σ$. Moreover, there exists a milder $\sim 2σ$ tension between similar predictions for the amplitude $S_8$ of matter fluctuations and its measurement in the local universe. As explanations relying on unresolved systematics have not been found, theorists have been exploring explanations for these anomalies that modify the cosmological model, altering early-universe-based predictions for these parameters. However, new cosmological models that attempt to resolve one tension often worsen the other. In this paper, we investigate a decaying dark matter (DDM) model as a solution to both tensions simultaneously. Here, a fraction of dark matter density decays into dark radiation. The decay rate $Γ$ is proportional to the Hubble rate $H$ through the constant $α_{\rm dr}$, the only additional parameter of this model. Then, this model deviates most from $Λ$CDM in the early universe, with $α_{\rm dr}$ being positively correlated with $H_0$ and negatively with $S_8$. Hence, increasing $α_{\rm dr}$ (and allowing dark matter to decay in this way) can then diminish both tensions simultaneously. When only considering Planck CMB data and the local SH0ES prior on $H_0$, $\sim 1$\% dark matter decays, decreasing the $S_8$ tension to $0.3σ$ and increasing the best-fit $H_0$ by $1.6$ km/s/Mpc. However, the addition of intermediate-redshift data (the JLA supernova dataset and baryon acoustic oscillation data) weakens the effectiveness of this model. Only $\sim 0.5$\% of the dark matter decays bringing the $S_8$ tension back up to $\sim 1.5 σ$ and the increase in the best-fit $H_0$ down to $0.4$ km/s/Mpc.

Alleviating the $H_0$ and $σ_8$ anomalies with a decaying dark matter model

TL;DR

The paper investigates a decaying dark matter model where DM decays into dark radiation at a rate Γ = α_dr H to jointly address the Hubble tension and the tension. By altering the early-universe expansion and reducing late-time matter density, the model increases and lowers , with α_dr governing the effect. Across data combinations, Planck-only favors tiny α_dr (≤0.003), while Planck+R18 can push α_dr to ~0.005±0.003, moderately alleviating both tensions; however, incorporating intermediate-redshift data (JLA+BAO) weakens the improvement and keeps tensions at ~2.5σ for and ~1.5σ for , indicating the model cannot fully resolve the anomalies with current data.

Abstract

The Hubble tension between the CDM-model-dependent prediction of the current expansion rate using Planck data and direct, model-independent measurements in the local universe from the SH0ES collaboration disagree at . Moreover, there exists a milder tension between similar predictions for the amplitude of matter fluctuations and its measurement in the local universe. As explanations relying on unresolved systematics have not been found, theorists have been exploring explanations for these anomalies that modify the cosmological model, altering early-universe-based predictions for these parameters. However, new cosmological models that attempt to resolve one tension often worsen the other. In this paper, we investigate a decaying dark matter (DDM) model as a solution to both tensions simultaneously. Here, a fraction of dark matter density decays into dark radiation. The decay rate is proportional to the Hubble rate through the constant , the only additional parameter of this model. Then, this model deviates most from CDM in the early universe, with being positively correlated with and negatively with . Hence, increasing (and allowing dark matter to decay in this way) can then diminish both tensions simultaneously. When only considering Planck CMB data and the local SH0ES prior on , \% dark matter decays, decreasing the tension to and increasing the best-fit by km/s/Mpc. However, the addition of intermediate-redshift data (the JLA supernova dataset and baryon acoustic oscillation data) weakens the effectiveness of this model. Only \% of the dark matter decays bringing the tension back up to and the increase in the best-fit down to km/s/Mpc.

Paper Structure

This paper contains 8 sections, 10 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Decaying dark matter model
  3. Background dynamics
  4. Calculation of $\Delta N_{\rm eff}$
  5. Effects on observables
  6. Methodology
  7. Results
  8. Discussion and conclusions

Figures (5)

  • Figure 1: Shown here are the effects of DDM on various observables. These plots were produced using a modified version of CAMB, fixing all $\Lambda$CDM parameters except $\Omega_{\rm dm, 0}$ and deriving $\Omega_{\Lambda,0}$ by imposing flatness (see Section \ref{['subsec:effect_observables']}). The blue line with $\alpha_{\rm dr} = 0$ represents a $\Lambda$CDM cosmology. Top: effect of non-zero $\alpha_{\rm dr}$ on the CMB TT power spectrum; left: effect on the matter power spectrum; right: the DDM expansion rate relative to $\Lambda$CDM.
  • Figure 2: Comparison between the standard $\Lambda$CDM and the DDM models: Constraints on various cosmological parameters along with their covariances when tested against the Planck data. The green bands represent the constraints on $H_0$ and $S_8$ coming from 2018ApJ...861..126R and 2017arXiv170801530D. The positive correlation between $H_0$ and $\alpha_{\rm dr}$ and the negative correlation $S_8$ and $\alpha_{\rm dr}$ can be seen here.
  • Figure 3: Comparison between the standard $\Lambda$CDM and the DDM models: Constraints on various cosmological parameters along with their covariances when tested against the Planck+R18. The green bands represent the constraints on $H_0$ and $S_8$ coming from 2018ApJ...861..126R and 2017arXiv170801530D. The correlations of $\alpha_{\rm dr}$ with $H_0$ and $S_8$ are more clearly visible here from the tilts of their contours. This data set combination also has the largest shift in $\Omega_m$, which helps relieve both tensions.
  • Figure 4: Comparison between the standard $\Lambda$CDM and the DDM models: Constraints on various cosmological parameters along with their covariances when tested against the Planck+JLA+BAO+R18. The green bands represent the constraints on $H_0$ and $S_8$ coming from 2018ApJ...861..126R and 2017arXiv170801530D.
  • Figure 5: The figures show the $\Lambda$CDM (blue) and DDM (red) constraints on the $H_0-S_8$ plane for two dataset combinations, Planck+R18 and Planck+R18+JLA+BAO. The green bands represent the 1 and 2 $\sigma$ constraints on $H_0$ and $S_8$ coming from 2018ApJ...861..126R and 2017arXiv170801530D. The scattered points are for the DDM model representing values of $\alpha_{\rm dr}$.