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A Solution to the Coincidence Puzzle of Ω_{B} and Ω_{DM}

Masaaki Fujii, T. Yanagida

TL;DR

This work links the baryon and dark matter densities via Affleck–Dine baryogenesis with late-time Q-ball decay, producing non-thermal LSPs and yielding a direct Ω_B/Ω_χ relation that depends primarily on low-energy parameters and a CP-violating phase δ_eff. The key result is Ω_B/Ω_χ ≈ 10^{3–4} (m_φ^2 / ⟨σv⟩_χ^{-1}) (m_p / m_χ) δ_eff, which matches observations for plausible masses and annihilation cross sections, while remaining insensitive to the Universe’s reheating history under specified conditions. The framework favors Higgsino- or Wino-like LSPs with large ⟨σv⟩, leading to distinctive direct/indirect detection signatures and a potential link to non-thermal dark matter explanations for cosmic-ray anomalies. The model also naturally avoids the gravitino problem due to entropy production from Q-ball decay, and it ties the initial φ amplitude to high-scale physics near the B−L breaking scale, offering testable low-energy consequences.

Abstract

We show that a class of Affleck--Dine baryogenesis directly relates the observed mass density of baryons, Ω_{B}, to that of dark matter, Ω_{DM}. In this scenario, the ratio of baryon to dark matter mass density is solely determined by the low energy parameters, except for an O(0.1) effective CP-violating phase. We find that Ω_{B}/Ω_{DM}=O(0.1) with reasonable parameters, which lies surprisingly just in the range of observation. This scenario is totally free from the cosmological gravitino problem, and independent of the detailed history of the Universe as long as it satisfies quite weak constraints.

A Solution to the Coincidence Puzzle of Ω_{B} and Ω_{DM}

TL;DR

This work links the baryon and dark matter densities via Affleck–Dine baryogenesis with late-time Q-ball decay, producing non-thermal LSPs and yielding a direct Ω_B/Ω_χ relation that depends primarily on low-energy parameters and a CP-violating phase δ_eff. The key result is Ω_B/Ω_χ ≈ 10^{3–4} (m_φ^2 / ⟨σv⟩_χ^{-1}) (m_p / m_χ) δ_eff, which matches observations for plausible masses and annihilation cross sections, while remaining insensitive to the Universe’s reheating history under specified conditions. The framework favors Higgsino- or Wino-like LSPs with large ⟨σv⟩, leading to distinctive direct/indirect detection signatures and a potential link to non-thermal dark matter explanations for cosmic-ray anomalies. The model also naturally avoids the gravitino problem due to entropy production from Q-ball decay, and it ties the initial φ amplitude to high-scale physics near the B−L breaking scale, offering testable low-energy consequences.

Abstract

We show that a class of Affleck--Dine baryogenesis directly relates the observed mass density of baryons, Ω_{B}, to that of dark matter, Ω_{DM}. In this scenario, the ratio of baryon to dark matter mass density is solely determined by the low energy parameters, except for an O(0.1) effective CP-violating phase. We find that Ω_{B}/Ω_{DM}=O(0.1) with reasonable parameters, which lies surprisingly just in the range of observation. This scenario is totally free from the cosmological gravitino problem, and independent of the detailed history of the Universe as long as it satisfies quite weak constraints.

Paper Structure

This paper contains 5 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The model
  3. Derivation of the relation of $\Omega_{B}$ and $\Omega_{DM}$
  4. Conditions for the relation to hold
  5. Conclusions and discussion

Figures (1)

  • Figure 1: The allowed region of reheating temperature for relation (\ref{['analytic-relation']}) to hold. The red (solid) line denotes the upper bound from Eq. (\ref{['T-condition3']}) with $|a_{g}|=1$ and $\sqrt{\alpha}=1/20$. The purple (dotted) line denotes the upper bound from the thermal mass term, Eq. (\ref{['T-condition2']}). Here, we take $c=1$, $f=10^{-5}$. This constraint becomes significantly weak if we do not adopt the first generation of up-type squark in the flat direction. The blue (dashed) lines represent the lower bounds from the Q-ball dominance condition given in Eq. (\ref{['condition-for-domination']}) with $\eta=0.3,\;|K|=0.1$ and $\eta=1\;,|K|=0.03$ from the bottom up, respectively. Throughout this calculation, we have used $m_{\phi}=1 {\rm ~TeV}$.