Parametric Coincidence in the Baryon to Dark Matter Ratio from Affleck-Dine Baryogenesis and UV Freeze-in Dark Matter

TL;DR

The work presents a framework in which the baryon and dark matter relic abundances are tied through their shared linear dependence on the reheating temperature $T_{ m rh}$ in supersymmetric theories. By pairing UV freeze-in dark matter production with Affleck-Dine baryogenesis, the authors show that the ratio $rac{ m ho_{DM}}{ ho_B}$ becomes largely independent of $T_{ m rh}$ when model parameters are $ ext{O}(1)$ and DM is a TeV-scale particle such as the gravitino. The paper details SUSY realizations (including Higgs-portal and axino UV freeze-in, and gravitino DM) and analyzes how Q-ball formation and NLSP decays can spoil or preserve the parametric coincidence, offering concrete scenarios—RH sneutrino AD and RPV AD—that maintain the link. The results provide a predictive mechanism for the observed near-equality of baryon and dark matter densities with implications for high-scale physics and cosmology, while outlining constraints from BBN, collider bounds, and indirect searches. Overall, the framework highlights a coherent UV-sensitive origin for both relic densities, reinforcing the relevance of $T_{ m rh}$-driven dynamics in the early Universe.

Abstract

We highlight that the observed concurrence between the baryon and dark matter relic densities can be explained via a parametric coincidence between two distinct production mechanisms: Affleck-Dine baryogenesis and dark matter UV freeze-in. In the Affleck-Dine mechanism, the baryon asymmetry is naturally proportional to the inflationary reheating temperature $T_{\rm rh}$, which also plays a critical role in setting the relic abundance of UV freeze-in dark matter. Since Affleck-Dine baryogenesis requires flat directions in the potential, the framework is inherently supersymmetric, offering compelling UV freeze-in dark matter candidates such as the gravitino. We outline scenarios in which $T_{\rm rh}$ simultaneously determines both relic abundances, resulting in a baryon-to-dark matter ratio of order unity that is largely insensitive to $T_{\rm rh}$. We also discuss the conditions required to avoid Q-ball formation or dark matter production by other mechanisms, such as NLSP decays, to preserve the parametric coincidence between baryon and dark matter abundances.

Figures (3)

• Figure 1: The dark matter abundance from UV freeze-in and the baryon abundance from the Affleck-Dine mechanism in terms of the reheating temperature $T_{\rm rh}$. Both abundances are proportional to $T_{\rm rh}$, so the ratio between them does not depend on $T_{\rm rh}$. With $\mathcal{O}(1)$ model parameters $R_\textrm{UV}$ and $R_{\rm AD}$ of eq. (\ref{['eq:nchi']}) and (\ref{['eq:Yphi']}), the ratio is naturally $\mathcal{O}(1)$ as in eq. (\ref{['ratio']}). We assume that the UV freeze-in portal and the operator that lifts the flat direction in the Affleck-Dine mechanism are both mass dimension five (i.e. corresponding to $n=4$ in the potential of eq. (\ref{['V']})) with the cut-off scales both identified as the reduced Planck mass $M_{\rm Pl}$.
• Figure 2: The plot shows the impact of varying the gravitino LSP mass $m_{3/2}$ and the reheat temperature $T_{\rm rh}$ on the ratio of $\Omega_{\rm DM}/\Omega_\textrm{B}$. It is assumed that the baryon abundance $\Omega_\textrm{B}$ arises from to Affleck-Dine baryogenesis with $\phi=\widetilde{\nu}_R$ and relic abundance of gravitino LSP is due to UV freeze-in $\Omega_{\rm DM}$. We assume that NLSP decays to gravitinos lead to a negligible contribution to $\Omega_{\rm DM}$, as is the case for our benchmark model with $\sin\theta_{\tilde{\nu}} = 0.1$ and $m_{\tilde{L}} = 5 m_{\tilde{\nu}_1}$ (see main text). Q-balls production will also be generically absent. As a result, the ratio of $\Omega_{\rm DM}/\Omega_\textrm{B}$ is constant with $T_{\rm rh}$ as discussed in Section \ref{['Sec2']}. The near-vertical lines indicate the $T_{\rm RH}$-independence of the ratio $\Omega_{\rm DM}/\Omega_\textrm{B}$, with the slight variation arising due to mild renormalisation effects.
• Figure 3: We consider the RPV flat direction such that the baryon asymmetry is set by RPV coupling $\lambda$ in eq. (\ref{['RpvAD']}), and the parameter $a_{\rm eff}$ implictly defined in eq. (\ref{['eq:aeff']}). We indicate parameter values that correctly reproduce the observed dark matter abundances (dashed lines) and baryon asymmetry (dotted lines) and via UV freeze-in of the gravitino and Affleck-Dine baryogenesis, respectively. The black solid line identifies both dark matter and baryon abundance are the observed values. Observational constraints are overlaid. The blue shaded region indicates the gravitino LSP lifetime does not lead to indirect detection constraints, and the grey region corresponds to where large $\lambda$ leads to washout of the asymmetry, both taken from Monteux:2014tia. While BBN limits can arise from NLSP (with mass $m_{\rm soft}$) decays to gravitinos, for the whole plot area shown, these are found not to be constraining. The yellow region indicates typical LHC limit on coloured superpartners, we take the conservative bound $m_{1/2}>2.4$ TeV ATLAS:2024lda. In the three panels we consider both gravity and gauge mediated type spectra, and the case in which the $\mathcal{O}(1)$ coefficients $R_{\rm AD}$ in the Affleck-Dine model are less than unity. Observe that viable scenarios exist in all cases, although the gravity mediated model with $R_{\rm AD}=1$ is most tightly constrained, requiring $T_{\rm rh}\sim10^9$ GeV.