Cosmology · April 2026
A Zero-Parameter Derivation of the Ultra-Light Dark Matter Mass
The fifth vacancy on the bridge line is dark matter. Its mass is 2.07×10⁻²² eV, oscillating at 49.9 nanohertz, abundance 23.6%. Two independent routes converge to the same component. NANOGrav's 15-year dataset already contains 20–30 complete periods.
Key Results
One mass, two routes, one prediction
The bridge line places the cosmological constant, the gravitational constant, and the Hubble rate on a single line with slope α⁻¹. It has a fifth vacancy, forced by the Galois symmetry of the underlying number field. The mass at that vacancy is 2.07×10⁻²² eV. A four-way cosmic partition independently predicts dark matter at 23.6% of the total energy budget: the gravitating, non-radiating component that acquired gravitational coupling but lost electromagnetic phase coherence before completing its second winding revolution. The oscillation frequency is 49.9 nHz; the period 232 days.
1
The bridge line has five positions; the fifth is unoccupied by any Standard-Model constant. A Galois-symmetric mass sits at 2.07×10⁻²² eV.
2
A four-way cosmic partition — radiation, baryons, coherent matter, dark matter — predicts the dark-matter share at 23.6%, matching observation.
3
A scalar field of this mass oscillates at 49.9 nHz with period 232 days. The soliton gravitational-wave frequency is 99.8 nHz.
4
The NANOGrav 15-year dataset is sensitive to frequencies up to 60 nHz and contains 20–30 complete oscillation periods at 49.9 nHz. No published analysis has searched for a monochromatic signal at exactly this frequency.
Kill Conditions
K1: NANOGrav null result for a monochromatic 49.9 nHz common-mode signal at expected amplitude — derivation falsified
K2: Lyman-α forest constraints ruling out m = 2.07×10⁻²² eV — bridge-line fifth position falsified
K3: Cosmological dark-matter abundance measured outside 23.6% ± 0.5% at CMB-S4 precision — four-way partition falsified