The unified Bound Dark Energy--Bound Dark Matter model: theory and constraints from DESI DR2

The unified Bound Dark Energy–Bound Dark Matter (BDE-BDM) model derives both the dark energy and the whole of the dark matter from a single supersymmetric $SU(3)$ gauge group with $N_f=6$ flavors. Gauge-coupling unification predicts the scale at which it condenses, $\text{Lc}=34_{-11}^{+16}$~eV, before any cosmological data are used, so the dark-energy sector adds no parameter to those of \LCDM\ and the dark-matter sector adds only one. Fitting DESI DR2 BAO, Planck CMB, Planck+ACT DR6 CMB lensing, and three supernova compilations (PantheonPlus, Union3.1, DES-Dovekie) gives, for Union3.1, $\text{Lc}=43.67\pm 0.13$~eV, inside the predicted range: a high-energy prediction met by a late-time measurement. The equation of state evolves to $w_0=-0.9262\pm 0.0005$ and never crosses the phantom divide. Relative to \LCDM\ the model lowers the DESI BAO ${\chi }^2$ by $2.95$–$3.67$ and the supernova ${\chi }^2$ by $2.53$–$4.07$, recovering $57\mathrm{\%}$–$71\mathrm{\%}$ of the total reduction that \wowa\ obtains by fitting two dark-energy parameters to the same data, and reaching the lower BAO ${\chi }^2$ of the two models for two of the three compilations. Its $\mathrm{\Delta }\mathrm{D}\mathrm{I}\mathrm{C}$ against \LCDM\ is strong for every compilation, $-8.28$ to $-7.47$, varying by $0.81$ where that of \wowa\ varies by $4.8$. Because the dark-energy sector adds no parameter to those of \LCDM, the likelihood gain survives the Occam penalty: $\ln B=+4.09$, $+4.12$, and $+4.83$ against \LCDM, where \wowa\ gives $-2.11$, $-0.26$, and $-0.56$. Among six models pairing a cosmological constant, the \wowa\ parametrization or bound dark energy with cold or bound dark matter, BDE-BDM has the largest Bayesian evidence.