Multi-Phase Dynamic Expansion Cycle (MPDEC)

Core Mechanism: Perturbation → Relaxation → Residual Bias

MPDEC is built on three physical components:

1. Horizon‑Adjacent Perturbations

Black holes generate small, localized metric disturbances through:

• internal plasma dynamics

• electromagnetic interactions

• horizon‑scale oscillations

These perturbations are ubiquitous and recur across cosmic time.

2. Causal Relaxation with Finite τ

Spacetime relaxes toward equilibrium with a characteristic timescale τ.

This is not instantaneous; it is governed by causal dissipative hydrodynamics.

3. Incomplete Recovery

If perturbations recur on timescales shorter than τ, spacetime retains a residual stress Π.

Coarse‑grained across cosmic black hole populations, this produces a Λ‑like acceleration.

Why MPDEC Mimics Λ at the Background Level

This is not a rhetorical hedge — it is a mathematical consequence of the causal relaxation equation.

In the overdamped regime, where

τ≪H-1,

the constitutive relation admits a stable fixed point:

Π→−3ζH,

with corrections suppressed by

O(τH)≈10-3–10−2 

for the empirically measured

τ≈0.2–0.4 Gyr.

Thus:

• Λ‑equivalence is a structural attractor, not a curve‑fit.

• Small deviations arise naturally from phase‑lag effects in the forcing.

• These deviations correlate with black hole activity histories.

This is why MPDEC is observationally indistinguishable from Λ at the background level, yet still falsifiable.

Mathematical Framework

MPDEC achieves full closure through the Israel–Stewart constitutive relation:

τ(dΠ/dt)+Π=−3ζH 

where:

• Π(z) is the deviation stress (the non‑Λ component)

• τ is the relaxation timescale

• ζ(z) is the response coefficient

• H is the Hubble expansion rate

Once τ is empirically extracted, ζ(z) is algebraically determined from data.

There are no free parameters left to tune.

Empirical Detection of the Relaxation Timescale τ

A central result of MPDEC is the extraction of a robust relaxation timescale:

τfast ≈0.2–0.4 Gyr.

This value:

• appears consistently across independent datasets

• is encoded directly in distance‑level observables

• is not the result of tuning

• sits naturally between black hole dynamical timescales and the Hubble time

The weighted mean,

τfast ≈0.26 Gyr,

yields exceptionally strong fits to expansion‑history data.

OCT (Microscopic)

• describes black hole interior dynamics

• predicts oscillation frequencies ω0∝M−1/2 

• provides horizon‑scale fluctuations δrs(t)

• makes falsifiable predictions

MPDEC (Macroscopic)

• treats horizon‑adjacent perturbations as localized strain sources

• applies causal relaxation dynamics

• coarse‑grains over cosmic populations

• produces Λ‑like behavior as a steady‑state limit

MPDEC does not depend on OCT being correct.

Theoretical Implications

If MPDEC is correct:

• Λ is emergent, not fundamental

• black holes influence cosmic expansion through classical strain

• spacetime has a memory horizon set by τ

• the near‑constancy of w arises naturally from overdamped relaxation

• the cosmological constant problem becomes irrelevant

MPDEC reframes cosmic acceleration as a dynamical, causal phenomenon.

Scope and Limitations

What MPDEC Addresses

• late‑time acceleration (z < 3)

• Λ‑equivalent steady‑state behavior

• connection between black hole dynamics and expansion history

What MPDEC Does Not Address

MPDEC does not model early‑universe rapid expansion.

Causal relaxation enforces rise‑time constraints that prevent inflation‑like behavior.

Current Status and Invitation for Review

The MPDEC framework includes:

• complete mathematical closure

• empirical extraction of τ

• astrophysical consistency checks

• forward‑amplitude validation

• combined driver analysis

• comprehensive falsifiability criteria

MPDEC is presented as a conservative, testable reinterpretation of cosmic acceleration grounded entirely in established physics.

Upcoming surveys — DESI, Euclid, Roman — will provide decisive tests within this decade.