A thermodynamic selection principle for a Yang–Mills–Higgs dark sector: structural unification with an emergent order parameter

The ΛCDM model successfully fits the expansion history of the Universe but treats dark matter(DM) and dark energy (DE) as independent, non-interacting components. We propose a structurallyunified dark sector in which both emerge as distinct effective phases of a single symmetry-breakingframework. The construction is guided by a thermodynamic selection heuristic: demanding that thedark-sector contribution to the local entropy current be extremal on Rindler horizons singles out aclass of stable, causal Lagrangians. The minimal renormalisable choice within this class contains anSU(2)D gauge symmetry and a global U(1)P Q symmetry, broken spontaneously by a scalar doubletand a scalar singlet, respectively. The three massive SU(2)D vector bosons provide cold dark matterthrough standard freeze-out, while the pseudo-Goldstone boson of the global symmetry acts asquintessence dark energy around a fixed vacuum offset. The order parameter of the broken phase,|Φ|, evolves with the Hubble expansion, leading to a smooth crossover in the dark-sector equationof state from w ≈ 0 to w ≈ −1 at redshift zc ∼ O(1). We derive the thermodynamic mappingfrom horizon entropy to the dark-sector Lagrangian, emphasising that it is a selection principlerather than a uniqueness theorem; identify the custodial symmetry that stabilises the gauge bosons;compute the DM annihilation cross-section including all relevant channels; and confront the modelwith direct-detection and collider limits. We present an expanded parameter-space analysis showinghow the crossover redshift zc, the self-interaction scale k∗, and the stochastic gravitational-wavebackground vary across the plausible range of couplings. Three falsifiable predictions are derived:(i) a characteristic deviation of w(z) from a constant, testable with DESI and Euclid; (ii) a scale-dependent suppression of the matter power spectrum at k ≳ 1 h Mpc−1 due to self-interactions ofthe DM, with the characteristic scale k∗ computed from the gauge coupling and DM mass; and(iii) a stochastic gravitational-wave background from a network of global strings, with a detailedspectrum calculation placing it in the sensitivity band of LISA and pulsar timing arrays, togetherwith a critical discussion of the theoretical uncertainties specific to global defects. We discuss thelimitations of the effective description, the prospects for a full Einstein–Boltzmann implementation,and clarify that the model offers structural unification within a single Lagrangian without claimingto resolve the cosmic coincidence problem from first principles.