From Immutable Past to Primordial Horizons: How Zero Frequency Seeds Dark Matter and Dark Energy

1 — Immutable Past → Zero Frequency

The axiom “the past is immutable” implies absolute stillness in time. A fully frozen event has a temporal frequency f = 0 Hz; no further phase change can occur. Quantum mechanics describes this as a wavefunction that has collapsed to a single eigenstate; general relativity observes an analogous effect at an event horizon, where outgoing signals are red‑shifted until a distant clock measures f_∞ → 0.

2 — Zero Frequency → Horizon Formation

Gravitational red‑shift relates local and distant frequencies through f∞ / flocal = √(1 – rs/r), where rs = 2GM/c2 is the Schwarzschild radius. When a distant observer measures f∞ = 0, the emitting surface sits precisely at r = rs. Thus a domain whose dynamics have frozen (frequency → 0) becomes, to the external world, a horizon—a black hole interior in everything but name.

3 — Primordial Horizons and Dark Matter

If such horizons formed during the high‑curvature moments of the early universe, they would survive as primordial black holes (PBHs). Because PBHs arise from geometry, not stellar collapse, they evade nucleosynthesis limits and remain promising cold‑matter candidates. Current surveys exclude much—but not all—of the PBH mass spectrum; narrow windows near 10⁻¹⁶–10⁻¹⁴ M_⊙ and ≈ 1–100 M_⊙ are still viable.

4 — Vacuum Energy in Horizons and Dark Energy

If black‑hole interiors store vacuum energy of negative pressure, every horizon contributes a small portion to the universe’s acceleration. Recent galaxy‑evolution studies show super‑massive black holes growing in lock‑step with cosmic expansion—evidence that horizons may indeed “couple” to dark energy.

5 — Putting It Together

• Immutable past ⇒ zero temporal frequency.
• Zero frequency ⇒ horizon condition (r = r_s).
• Primordial horizons ⇒ PBH population (dark matter).
• Horizon vacuum energy ⇒ global negative pressure (dark energy).

A single logical thread—frozen time domains becoming horizons—can therefore account, in principle, for both missing mass and the universe’s accelerated stretch. Forthcoming microlensing campaigns, gravitational‑wave catalogs, and precision cosmic‑expansion surveys will test this joint explanation.

References

1. “New Mass Window for Primordial Black Holes as Dark Matter,” arXiv (2024)
2. Green A.M., “Primordial Black‑Hole Microlensing Constraints,” Inspire HEP (2024)
3. Phys.org, “Study Links Black Holes to Dark Energy” (2024)
4. University of Michigan News, “Evidence Mounts for Dark Energy from Black Holes” (2024)
5. Phys. Rev. D 110 (2024): “New Mass Window for PBHs from Evaporation Physics”