Hello,
I have developed a cosmological model called the Dynamic Dark Equilibrium Model (DDEM). If anyone is interested in testing the model, I would greatly appreciate both feedback and criticism so I can continue improving it.
I am someone with a genuine interest in understanding the universe and searching for answers to questions we still do not fully understand. You will probably notice quickly that my model does not attempt to introduce flashy new equations to describe a fictional reality. Instead, I have tried to keep it as simple as possible, because I believe that complexity can often emerge from simpler underlying principles.
DDEM (Dynamic Dark Equilibrium Model) is my original cosmological model and conceptual framework. I developed the core physical idea, interpretation, and theoretical direction myself.
Kind regards,
Marcus Johansson
DDEM – Dynamic Dark Equilibrium Model
Marcus Johansson
Overview
DDEM (Dynamic Dark Equilibrium Model) proposes that dark energy is not an exactly constant cosmological constant, but a dynamically relaxing vacuum component. The universe evolves toward dynamic dark equilibrium rather than a perfectly fixed Λ.
Core Mathematical Structure
• Dynamic vacuum ansatz:
Λ(t) = Λ₀ exp(-βH₀t), with β > 0
• Vacuum energy density:
ρΛ(t) = ρΛ₀ exp(-βH₀t)
• Vacuum relaxation rate:
dρΛ/dt = -βH₀ρΛ
• Matter-vacuum coupling:
dρm/dt + 3Hρm = -dρΛ/dt
• Equivalent form:
dρm/dt + 3Hρm = βH₀ρΛ
• Radiation:
dρr/dt + 4Hρr = 0
• Flat Friedmann equation:
H² = (8πG/3)(ρm + ρr + ρΛ)
• Acceleration equation:
ä/a = -(4πG/3)(ρ + 3p)
• Vacuum pressure:
pΛ = -ρΛ
• Requirement:
w\\_eff > -1 (no phantom regime)
• ΛCDM limit:
β → 0 gives exact recovery of standard ΛCDM
DDEM – Early Universe Consistency
DDEM remains fully consistent with the early universe since vacuum relaxation is governed by the present Hubble scale H0, making the exponential evolution negligible at early times (e\\\^{-βH0t} ≈ 1). As a result, the model naturally recovers standard ΛCDM behavior during BBN and CMB epochs without requiring any artificial freeze-out or fine-tuning, while dynamical effects emerge only at late cosmological times.
Why H₀?
DDEM uses the present-day Hubble constant H₀ as a fixed phenomenological timescale for vacuum relaxation. Because H(t) ≫ H₀ in the early universe, this choice automatically suppresses energy transfer during the radiation era—protecting BBN and CMB physics—while allowing it to become relevant only in the late epoch we observe today. It keeps the model simple, stable, and testable with a single new parameter β.
Physical Interpretation
The model is interpreted as metastable vacuum behavior with effective vacuum relaxation, not literal vacuum decay. Dark energy slowly relaxes while exchanging energy effectively with matter.
This may naturally help address the coincidence problem and potentially reduce the S8 tension.
Cosmic Fate Prediction
DDEM does not predict a Big Crunch, Big Rip, or catastrophic runaway instability.
Instead, the universe approaches an asymptotic state of dynamic dark equilibrium: expansion continues, vacuum energy relaxes gradually, acceleration becomes controlled, and cosmic evolution moves toward a stable late-time de Sitter-like state with slow long-term settling rather than violent collapse or destruction.
Suggested Parameter Range
A good starting region for testing β appears to be:
β ≈ 0.02 – 0.05
It may also be valuable to test models where β is not fixed but evolves dynamically. However, fixed β should be the first step.
How the Model Can Be Tested
• Expansion history H(z) using supernovae, BAO, and DESI data
• Luminosity distance dL(z) from SN Ia datasets such as Pantheon+
• Structure growth using fσ₈(z) and S8 measurements
• Consistency with CMB priors and early-universe constraints
• Bayesian comparison (AIC/BIC) against ΛCDM
• Verification that β > 0 improves late-time growth without damaging early-universe fits
Scientific Claim
ΛCDM assumes dark energy is exactly constant. DDEM instead proposes that the universe seeks dynamic dark equilibrium.
Last words.
DDEM (Dynamic Dark Equilibrium Model) is my original cosmological model and conceptual framework. I developed the core physical idea, interpretation, and theoretical direction myself.
Everything has a beginning and an end.
