A Causal Spacetime‑Relaxation Interpretation of Cosmic Acceleration
MPDEC proposes that late‑time cosmic acceleration emerges from causal spacetime relaxation driven by repeated horizon‑adjacent perturbations associated with black hole dynamics. Using only standard General Relativity and Israel–Stewart causal hydrodynamics, the framework shows how incomplete relaxation between perturbations produces a steady‑state negative‑pressure bias that mimics Λ at the background level. MPDEC is mathematically closed, empirically anchored, and falsifiable through near‑term cosmological surveys and black‑hole activity reconstructions.
The Multi‑Phase Dynamic Expansion Cycle (MPDEC) reframes cosmic acceleration as an emergent phenomenon rather than a fundamental constant. Instead of introducing new fields or modifying Einstein’s equations, MPDEC treats Λ‑equivalent behavior as the long‑term outcome of spacetime’s causal response to repeated, localized perturbations near black hole horizons.
The framework operates entirely within established physics. It uses the Israel–Stewart formalism — the same causal hydrodynamic machinery applied in neutron star physics and relativistic fluid dynamics — to model how spacetime relaxes toward equilibrium with a finite timescale τ.
When perturbations recur faster than τ, spacetime never fully relaxes. The residual stress accumulates into a stable negative‑pressure bias that, when coarse‑grained across cosmic black hole populations, produces an effective equation‑of‑state parameter
weff≈−1 .
MPDEC does not depend on any single model of black hole microphysics. It shows that black holes are involved. OCT proposes one possible manifestation of this involvement.
MPDEC is built on three physical components:
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.
Spacetime relaxes toward equilibrium with a characteristic timescale τ.
This is not instantaneous; it is governed by causal dissipative hydrodynamics.
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.
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.
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.
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.
When ζ(z) is reconstructed using the same τ, it aligns closely with independent histories of black hole activity:
peak at z ≈ 1.5–2.5 (cosmic noon)
broad asymmetric profile matching AGN and BHARD reconstructions
no additional tuning required
This multi‑way consistency suggests that MPDEC is detecting a real astrophysical signal rather than fitting noise.
A key sanity check confirms that the implied local stress amplitude is extremely small:
Πloc ≈10-3 Pa,
fifteen orders of magnitude below natural curvature scales near horizons.
MPDEC decomposes the forcing into:
oscillatory forcing from horizon‑localized dynamics
accretion forcing from black hole growth
A non‑negative least squares fit yields:
B/A≈0.10,
indicating oscillatory dynamics dominate by roughly an order of magnitude.
Accretion contributes a bounded secondary component but does not destabilize the framework.
MPDEC and OCT operate at complementary scales:
describes black hole interior dynamics
predicts oscillation frequencies ω0∝M−1/2
provides horizon‑scale fluctuations δrs(t)
makes falsifiable predictions
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.
It requires only that horizon‑adjacent perturbations exist and recur faster than τ.
Calculations show that the MPDEC response coefficient mirrors the redshift observed in independent datasets. Some minor variance is to be expected due to distance and intermediary effects.
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.
late‑time acceleration (z < 3)
Λ‑equivalent steady‑state behavior
connection between black hole dynamics and expansion history
MPDEC does not model early‑universe rapid expansion.
Causal relaxation enforces rise‑time constraints that prevent inflation‑like behavior.
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.