In our framework, the cosmic membrane has evolved dramatically from its violent birth to its current gentle oscillation. This chronology reveals how the universe tuned itself to play its fundamental melody.
The Violent Birth
The brane appears at the Big Bang with quasi-Planckian tension τ_BB ~ 10⁵⁰ J/m²—a membrane stretched to breaking point, vibrating with pure energy.
Phase I - Trans-membrane Inflation (0 - 10⁻³⁴ s)
The colossal excess tension fuels exponential expansion. The membrane expands like a soap bubble blown by a hurricane, creating space from dimensional nothingness.
Phase II - Brane Reheating (10⁻³⁴ - 10⁻³² s)
Tension drops brutally via massive production of dark matter/anti-dark matter pairs in the bulk. This “quantum evaporation” dissipates excess energy, leaving residual tension around 10³⁰ J/m².
Phase III - Slow Stabilization (10⁻³² s - 100 Myr)
Tension relaxes logarithmically toward its current value. Like a violin string being tuned, the membrane seeks its natural frequency.
The Awakening of Oscillations
Only when τ becomes “loose enough” does the fundamental mode enter the T ~ 2 Gyr band. Oscillation starts about 1 Gyr after the Big Bang—exactly when Ringermacher & Mead observe the first oscillation in scale factor a(t)!
This temporal coincidence is no accident: it’s the moment when the universe, finally tuned, begins playing its fundamental melody.
The Living Universe
Our final vision: the cosmos is not an inert theater but a living organism:
| Phase | Time | Description |
|---|---|---|
| Birth | Big Bang | Maximum tension, first breath |
| Childhood | 0-1 Gyr | Relaxation, frequency tuning |
| Maturity | 1-50 Gyr | Established oscillations (we are here) |
| Old Age | 50-100 Gyr | Progressive damping |
| Silence | >100 Gyr | Strings relax, space forgets distance |
The Tension Calibration
The time for one complete oscillation follows the universal law:
\[T = 2π\sqrt{\frac{M_{osc}}{k_{eff}}} = 2π\sqrt{\frac{f_{osc} M_{DM,tot}}{τ_0}}\]Inverting for the observed period T = 2.0 Gyr:
\[τ_0 = f_{osc} M_{DM,tot} \left(\frac{2π}{T}\right)^2 = 7.0 × 10^{19} \text{ J/m}^2\]This value, neither arbitrary nor adjusted, emerges naturally from the system’s physics.
MONDian Gravity: Lazy Space
Beyond masses, in vast cosmic voids, spacetime becomes “lazy”—it resists movement differently. This laziness manifests as a threshold acceleration:
\[a_0 = \frac{cH_0}{2π} × ξ = 1.1 × 10^{-10} \text{ m/s}^2\]The factor ξ ≃ 1.05 encodes the informational content of the horizon—how many quantum “bits” define each cell of space.
Local Anisotropies: Mapping Tension
Local tension variation induces variation in the Hubble “constant”:
\[\frac{δH}{H} ≃ \frac{1}{2} \frac{δτ}{τ_0} ≈ 10^{-4}\]where δτ/τ₀ represents the local tension contrast, estimated at ~2×10⁻⁴ in the Local Supercluster vicinity. A future program capable of measuring H₀ directionally at 0.05% precision over 10° patches could reveal this cosmic tension map—regions where the membrane is tighter expand slightly faster!