Unification of Dark Matter and Dark Energy through a Chiral Condensate of Coupled Dirac Oscillators

The standard cosmological paradigm (ΛCDM) faces severe small-scale observational tensions—specifically the Core-Cusp and missing satellites problems—and suffers from a fundamental disconnection regarding the microscopic nature of Dark Energy. In this work, we develop a theoretical framework where the quantum vacuum is modeled as a macroscopic condensate of coupled fermionic oscillators (matter-antimatter pairs in the Weyl basis). We demonstrate analytically that the mass coupling induced by the Higgs mechanism generates an effective energy-momentum tensor that unifies the dark sector: time-averaged inertia reproduces the Dark Matter equation of state w≈ 0, while the coupling's tension energy produces a negative pressure identical to the Cosmological Constant Λ. We derive the quantum pressure of this condensate and incorporate it into the Jeans Equation, showing that it suppresses gravitational collapse below a critical length. This generates a natural cut-off in the power spectrum $P(k)$ and results in rotation curves with flat cores, consistent with astrophysical observations without the need to postulate new exotic particles.