Baryon–Dark Matter Correspondence

• Baryon–Dark Matter Correspondence is the study of unified models that explain why baryonic and dark matter densities are nearly equal, suggesting shared origins and dynamical connections.
• Models such as asymmetric genesis, scalar relaxation, and mirrored sectors drive parameter locking and predict dark matter masses near the proton mass.
• This framework offers testable predictions via astrophysical scaling laws, collider signals, and direct detection experiments, guiding future research directions.

Baryon–Dark Matter Correspondence refers to the observed near-equality, up to an O(1) factor, of the mass densities of baryonic matter ($\Omega_B$) and dark matter ($\Omega_{\rm DM}$) in the Universe. This coincidence is highly nontrivial from the perspective of standard cosmology, where the origins of $\Omega_B$ (established by baryogenesis) and $\Omega_{\rm DM}$ (traditionally by thermal freeze-out) are in principle independent physical processes. Correspondence models aim to provide a dynamical or symmetry-based explanation for $\Omega_{\rm DM} \sim \Omega_B$, often relating the genesis, stability, or abundance of dark matter and baryons either through unified mechanisms, shared quantum numbers, or statistical/anthropic selection.

1. Theoretical Approaches Linking Baryon and Dark Matter Densities

Multiple frameworks address the correspondence, typically by correlating number densities or mass scales:

• Asymmetric Genesis Models: These generate a dark sector particle–antiparticle asymmetry, typically simultaneous with (or proportional to) the baryon asymmetry, with the final relic densities set by the same underlying process or quantum number. In such scenarios, dark matter masses are often predicted to be near the proton mass to realize $$\Omega_{\rm DM}/\Omega_B \sim m_{\rm DM}/m_p \sim \mathcal{O}(1-5)$$ (Gu et al., 2017, Graesser et al., 2011, Gu et al., 2010, Volkas, 2013, Walker, 2012). Examples include:
  • Quark–Seesaw + $U(1)_X$ integral asymmetry models (Gu et al., 2017)
  • Baryon-symmetric universe frameworks (Volkas, 2013)
  • Extended technicolor with dark atom formation via sphaleron transfer (Beylin et al., 2024)
  • Models gauging baryon number (Duerr et al., 2013, Ma, 2020)
• Scalar Relaxation and Dynamical Mechanisms: A light scalar dynamically ties together baryon and dark matter densities by adjusting fundamental parameters (e.g., mass scales, couplings) so that $\rho_{\rm DM}/\rho_B$ equilibrates to an O(1) value set by model-specific couplings. The ratio is often determined by the structure of the scalar potential and matter couplings, independent of the precise dark matter production mechanism (Brzeminski et al., 2023, Banerjee et al., 2024).
  • QCD axion “scanner” models exploit the exponential sensitivity of proton and axion mass to a dynamical field, achieving $\Omega_{\rm DM}/\Omega_B$ as a discrete, model-predicted constant (Banerjee et al., 2024).
• Parametric Coincidence and Production Channel Locking: Some constructions appeal to two or more yield mechanisms (e.g., Affleck–Dine baryogenesis for baryons and UV freeze-in or moduli decay for dark matter) that, while physically unrelated, yield relics proportional to a shared cosmological parameter—often the reheating temperature $T_{\rm rh}$. When both yields are proportional to $\Omega_{\rm DM}$0, their ratio is determined by coupling and mass prefactors alone, and is insensitive to the precise value of $\Omega_{\rm DM}$1, explaining $\Omega_{\rm DM}$2 robustly (Chang et al., 3 Jun 2025, Kane et al., 2011, Allahverdi et al., 2010).
• Mirror/Dual/QCD-Related Models: Frameworks with mirrored or sequestered gauge sectors (e.g., mirrored SU(5) unification (Ibe et al., 2019), heavy dark baryons in hidden MSSM-like sectors (Rosa et al., 2022)) naturally link the dark baryon mass to the QCD scale, and assign comparable baryon asymmetries to each sector, thus producing $\Omega_{\rm DM}$3 despite otherwise unrelated mass scales.
• Anthropic and Statistical Selection: Models positing random angular field values for baryon and dark matter densities across the multiverse can statistically explain the observed $\Omega_{\rm DM}$4 as a natural outcome of uniform measure, given the sole anthropic requirement of fixed baryonic density in galaxies at collapse (McDonald, 2012).

2. Unified Asymmetry and Quantum Number Flow

A recurring theme is the existence of a single conserved or approximately conserved quantum number whose redistribution between the visible (baryon) and hidden (dark sector) particles underpins relic densities:

• Gauged Baryon Number: Promoting baryon number to a local symmetry (typically $\Omega_{\rm DM}$5) not only renders the proton stable but introduces new fields that carry baryon number in both sectors. After spontaneous symmetry breaking, a residual discrete symmetry stabilizes the lightest dark sector particle carrying baryon number, naturally providing a dark matter candidate (Duerr et al., 2013, Ma, 2020). Simultaneous Affleck–Dine or other mechanism-driven asymmetry ties $\Omega_{\rm DM}$6 and $\Omega_{\rm DM}$7.
• Sphaleron Interplay and Operator Transfer: In scenarios with nonstandard sphalerons (e.g., in extended gauge sectors or technicolor models), anomaly-induced processes redistribute baryon number and hidden-sector charge, locking the generated asymmetries and tightly correlating $\Omega_{\rm DM}$8 to particle quantum numbers, sphaleron transfer coefficients, or ratios of anomaly coefficients (Beylin et al., 2024, Walker, 2012, Volkas, 2013).
• First-Order Phase Transition and Bubble Nucleation: If a “generative” sector undergoes a strong first-order phase transition, bubble walls can source an asymmetry in a generalized baryon charge $\Omega_{\rm DM}$9 (with $\Omega_B$0 exactly conserved, $\Omega_B$1 violated). Post-transition, $\Omega_B$2 is shared equally between baryonic and dark sectors, ensuring $\Omega_B$3 (Volkas, 2013).

3. Predictive Power for the $\Omega_B$4 Ratio

Many baryon–dark matter correspondence models yield concrete predictions or retrodictions for the observed ratio of cosmic mass densities:

• Mass Fixing from Yield Locking: When $\Omega_B$5 is ensured by symmetry or transfer dynamics, the relic mass ratio is set by

$\Omega_B$6

demanding $\Omega_B$7 few GeV for the observed cosmic value (Gu et al., 2017, Volkas, 2013, Gu et al., 2010, Allahverdi et al., 2013, McDonald, 2012).

• Discrete Combinatorial Predictions: In relaxation-based or composite axion models the ratio is a function of group-theoretic integer parameters, e.g.,

$\Omega_B$8

achieving the observed $\Omega_B$9 exactly when $\Omega_{\rm DM}$0 (Banerjee et al., 2024).

• High-Scale Parameters and Portal Suppression: In mirrored or heavy hidden sector models, $\Omega_{\rm DM}$1 arises from ratios of scales (e.g., QCD scales, reheating temperatures, SUSY-breaking scales), and can be held within the observed window across a large parameter range due to power-law or logarithmic scaling (Rosa et al., 2022, Ibe et al., 2019).
• Statistical Predictivity: In random field/anthropic frameworks the probability $\Omega_{\rm DM}$2 is a function determined by field measure and model exponents, making the observed $\Omega_{\rm DM}$3 a plausible statistical outcome without tuning (McDonald, 2012).

4. Phenomenological and Cosmological Consequences

Baryon–dark matter correspondence models predict several classes of observables:

Phenomenon	Signature / Testability	Reference
GeV-scale (asymmetric) dark matter	Accessibility in sub-keV threshold direct detection, efficient annihilation of symmetric $\Omega_{\rm DM}$4 component	(Gu et al., 2017)
Fifth-force or equivalence-principle violation	Light scalar mediating $\Omega_{\rm DM}$5 Yukawa forces; deviations from Newtonian gravity at sub-mm distances	(Banerjee et al., 2024, Brzeminski et al., 2023)
Collider signals of dark sector	Long-lived multi-charged particles, dijet or invisible $\Omega_{\rm DM}$6 resonances, missing energy events, production of heavy messenger quarks or leptons	(Walker, 2012, Volkas, 2013, Ma, 2020, Beylin et al., 2024)
Axion and dark photon searches	Axion decay constant and kinetic mixing within reach of cavity/helioscope and low-threshold experiments	(Banerjee et al., 2024, Ibe et al., 2019)
CMB and large scale structure	Isocurvature constraints (via Affleck–Dine phase), extra $\Omega_{\rm DM}$7 in dark sectors	(Rosa et al., 2022)

Additional signatures include cosmic-ray anomalies (e.g., from dark atom catalysis), primordial black hole mergers (direct collapse models) (García-Bellido et al., 2019), and indirect detection via suppressed but nonzero dark matter decay rates (Ma, 2020).

5. Astrophysical and Cosmological Scaling Laws

Beyond microscopic genesis models, empirical regularities in galaxy and cluster dynamics provide macro-scale evidence for baryon–dark matter correspondence:

• Radial Acceleration and Central Surface Density Relations: Analytic expressions in $\Omega_{\rm DM}$8CDM for $\Omega_{\rm DM}$9 vs $\Omega_{\rm DM} \sim \Omega_B$0 reproduce observed nontrivial correlations, showing that for a wide range of galaxies the distribution of dark matter is determined entirely by that of the baryons, once the baryon fraction and universal halo profile are set (Chan, 2017).
• Universal Virial and Central Mass Relation: High-precision power-law scaling, $\Omega_{\rm DM} \sim \Omega_B$1 (virial, galaxies to clusters) and $\Omega_{\rm DM} \sim \Omega_B$2 (central, both), with scatter $\Omega_{\rm DM} \sim \Omega_B$3 dex, represent "phenomenological correspondences" that must be addressed by any successful theory and may suggest deeper interplay or hidden dynamics beyond gravity alone (Chan, 2022).

6. Statistical and Anthropic Arguments

A statistical approach, whereby baryon and dark matter densities scan independently across domains or universes, predicts a distribution for $\Omega_{\rm DM} \sim \Omega_B$4 sharply peaked at $\Omega_{\rm DM} \sim \Omega_B$5 for natural exponents in the scaling $\Omega_{\rm DM} \sim \Omega_B$6, assuming observer selection depends only on baryon collapse density: $\Omega_{\rm DM} \sim \Omega_B$7 rendering the observed ratio natural even without a dynamical tie, provided dark matter abundance does not anthropically limit observers (McDonald, 2012).

7. Outstanding Questions and Future Prospects

Intrinsic to many correspondence models is the prediction—or retrodiction—of additional experimental and cosmological signatures:

• Direct detection of sub-GeV dark matter, possible only with new detector technologies targeting minute recoil energies (sub-keV) (Gu et al., 2017).
• Axion and axion-like particle searches probing decay constants and couplings relevant to cosmological relaxation mechanisms (Banerjee et al., 2024).
• Detection of fifth-force or equivalence-principle violation signals for models with light scalars connecting baryon and dark matter mass scales (Brzeminski et al., 2023).
• Collider searches for long-lived exotic particles with unique signatures such as highly-ionizing tracks or displaced vertices (Beylin et al., 2024, Walker, 2012).
• Precision cosmology measurements (CMB, isocurvature, $\Omega_{\rm DM} \sim \Omega_B$8) set constraints on sequestered or mirrored sectors (Rosa et al., 2022).

A robust baryon–dark matter correspondence framework thus provides both a unification of cosmic matter abundances and a suite of testable predictions at cosmological, astrophysical, and laboratory scales. The diversity of viable correspondence mechanisms highlights the importance of multifaceted experimental probes in isolating the true physical connection between visible and dark matter.