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Lyman-$α$ Forest Constraint on Dark Matter from Dark Sector Decay

Si-Yuan Zhao, Yi-Cheng Dai, Wei Liao, Yi-Song Lu

Abstract

By exploiting small-scale structure formation probed by Lyman-$α$ forest observations, we study constraints on a model of dark matter from dark sector decay. We compute the phase space distribution of the dark matter and the linear matter power spectrum. We map the non-thermal dark matter distribution in this dark matter model to an approximate thermal warm dark matter distribution, and use this approximation to obtain a constraint from the Lyman-$α$ forest observation. We combine the latest Lyman-$α$ forest bounds with the constraint from the Big Bang Nucleosynthesis. As these two probes offer highly complementary constraints, we impose strong limits on sub-GeV dark matter. Consequently, masses lighter than $\sim 10^{-1}$ GeV are excluded, thereby significantly limiting the allowed parameter space. More broadly, our findings demonstrate the utility of small-scale structure observations in testing non-thermal dark matter paradigms, offering valuable insights for exploring a wider class of late-time decay models.

Lyman-$α$ Forest Constraint on Dark Matter from Dark Sector Decay

Abstract

By exploiting small-scale structure formation probed by Lyman- forest observations, we study constraints on a model of dark matter from dark sector decay. We compute the phase space distribution of the dark matter and the linear matter power spectrum. We map the non-thermal dark matter distribution in this dark matter model to an approximate thermal warm dark matter distribution, and use this approximation to obtain a constraint from the Lyman- forest observation. We combine the latest Lyman- forest bounds with the constraint from the Big Bang Nucleosynthesis. As these two probes offer highly complementary constraints, we impose strong limits on sub-GeV dark matter. Consequently, masses lighter than GeV are excluded, thereby significantly limiting the allowed parameter space. More broadly, our findings demonstrate the utility of small-scale structure observations in testing non-thermal dark matter paradigms, offering valuable insights for exploring a wider class of late-time decay models.

Paper Structure

This paper contains 15 sections, 40 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Momentum Distribution of DM from Dark Sector Decay
  3. Thermal WDM approximation to DM distribution
  4. Velocity Dispersion
  5. Linear Transfer Function
  6. Lyman-$\alpha$ forest constraint on the model
  7. Velocity Dispersion Constraints
  8. Verification via Linear Power Spectrum
  9. Conclusions
  10. Calculation
  11. Decay Amplitude of $\phi \to N\chi$
  12. Derivation of the Collision Terms
  13. Approximations
  14. Zero-momentum Approximation
  15. Equivalent WDM Approximation

Figures (14)

  • Figure 1: Schematic flowchart of the $\chi$ DM production mechanism. The heavy parent particle $\phi$ first freezes out from the SM thermal bath and subsequently decays into the DM particle $\chi$.
  • Figure 2: Unperturbed background comoving phase-space distribution of the $\chi$ DM after production is completed. The horizontal axis represents the dimensionless comoving momentum $q/m_\chi$. In all panels, the parameters are fixed at $y_{\mathrm{DS}} = 10^{-12}$ and $m_N = 1\,\mathrm{GeV}$. The upper panels illustrate the distributions for a fixed $m_\phi = 1000\,\mathrm{GeV}$ with varying $m_\chi \in \{10, 1, 0.1\}\,\mathrm{GeV}$. The lower panels display the scenarios for a fixed $m_\chi = 1\,\mathrm{GeV}$ with varying $m_\phi \in \{10, 100, 1000\}\,\mathrm{GeV}$.
  • Figure 3: Same as Fig. \ref{['fig:Fchi1']}, but for varying decay couplings $y_{\mathrm{DS}} \in \{10^{-11}, 10^{-12}, 10^{-13}\}$. The other parameters are fixed at $m_\phi = 1000\,\mathrm{GeV}$, $m_\chi = 1\,\mathrm{GeV}$, and $m_N = 1\,\mathrm{GeV}$.
  • Figure 4: Comparison of the normalized unperturbed background comoving phase-space distributions between this model (red solid lines) and the equivalent thermal WDM model (blue dashed lines). The horizontal axis represents the dimensionless comoving momentum $q/m_\chi$. The masses of the parent particle and the associated decay product are fixed at $m_\phi = 1000\,\mathrm{GeV}$ and $m_N = 1\,\mathrm{GeV}$ across all panels. The upper, middle, and lower rows correspond to coupling constants of $y_{\mathrm{DS}} = 10^{-13}$, $10^{-12}$, and $10^{-11}$, respectively. The left, center, and right columns represent DM masses of $m_\chi = 0.01\,\mathrm{GeV}$, $1\,\mathrm{GeV}$, and $100\,\mathrm{GeV}$, respectively.
  • Figure 5: Comparison of the numerical transfer functions between our model and its equivalent WDM counterpart, obtained from CLASS numerical calculations. The chosen DM masses $m_\chi \in \{0.01, 1, 10\}\,\mathrm{GeV}$ correspond to effective thermal masses of $m_{\mathrm{eff}} \simeq 0.1$, $5$, and $25\,\mathrm{keV}$, respectively. Other parameters are fixed at $m_\phi = 1000\,\mathrm{GeV}$, $y_{\mathrm{DS}} = 10^{-12}$, and $m_N = 1\,\mathrm{GeV}$.
  • ...and 9 more figures