Dark matter as a relativistic vacuum condensate: its two-mode spectrum, stress–energy tensor, a Harmonic Coherence interaction and a programme of tests

We study dark matter as a relativistic complex scalar condensate whose collective Bogoliubov phonons (WIMQs) are its excitations. We derive the two-mode excitation spectrum and the full stress–energy tensor, show that the condensate is radiation-like early and cold today, and link the extra radiation at nucleosynthesis directly to the size of galaxy cores. We present a benchmark parameter set (boson mass 3×10⁻²⁰ eV, core radius 0.22 kpc) that satisfies nucleosynthesis, Lyman-α, colliding-cluster and black-hole-spin constraints at once, and lies in a narrow mass window that black-hole spin measurements can close. A Harmonic Coherence interaction and a programme of gravitational, lensing and laboratory tests are proposed.