Dark Matter

Astrophysical observations indicate that visible matter accounts for only a fraction of the mass required to explain galactic rotation curves and cluster dynamics. In the standard model, this necessitates invoking entirely new, undetected particle species (WIMPs, axions, sterile neutrinos).

Topological Dark Matter

The CPT framework does not require postulating new elementary fields. Instead, dark matter candidates emerge naturally as topologically stable torus knots possessing specific properties:

• — required for the knot to be a single, stable continuous structure.
• Net electromagnetic winding — making it electromagnetically dark.
• — providing a nonzero self-link and consequently a significant gravitational mass.

The Neutrality Constraint

A single knot has non-zero charge. Achieving zero charge requires canceling windings. A structure with would be neutral, but since , these are links rather than single knots, rendering them unstable.

Because a single stable knot cannot easily satisfy both and exact EM cancellation, dark matter in the CPT framework likely consists of bound states — pairs of knots whose aggregate electromagnetic field cancels externally while retaining a large combined gravitational mass.

CMB Implications

Additionally, the intrinsic geometry of the S³ universe alters the acoustic oscillation scale in the CMB. This geometric effect may account for some of the clustering signals traditionally attributed to dark matter, reducing the required abundance of these topological condensates.