QTT Dark-Sector Alternatives: Candidate Vacuum Capacity, Renewal Dust, and the H1 Failure Boundary

Reference: 10.5281/zenodo.17527179

In the standard cosmological model (ΛCDM), two mysterious components dominate the universe:

• Dark energy, usually modelled as a cosmological constant or exotic fluid.
• Dark matter, usually modelled as new, cold particles (WIMPs, axions, etc.).

QTT studies a different source model built from vacuum capacity, endurance/renewal mechanics, and a low-acceleration branch. The presently tested cluster-lensing implementation failed its H1 out-of-sample cases, so this archive is a candidate-construction record rather than a demonstrated replacement for the dark sector.

1. Dark energy with a vacuum–capacity law fixed by the Planck four–cell (no tuning), and
2. Dark matter with a combination of
   • extra gravitational terms from the endurance (renewal) mechanics, and
   • a natural MOND–like low–acceleration scale from the two–clock geometry, plus a purely gravitational “renewal dust” component.

Below, I’ll walk through the key boxed equations and then highlight the concrete tests that distinguish QTT from ΛCDM.

1. Dark energy → vacuum law from the Planck four–cell

1.1. Unified Equilibrium Law (UEL): Planck 4–cell capacity

QTT treats the Planck 4–cell as the primitive “capacity unit” of spacetime. The elementary four–volume is

Equation

V^(4)_quant = 4π ℓ_P⁴.

One such four–cell carries the Planck energy. QTT writes the Unified Equilibrium Law as

Equation

E_P := m_P c² = ℏ ω_P = ρ^(4) (4π ℓ_P⁴)

Here is a universal four–density (capacity per four–volume). This ties energy, Planck mass, Planck frequency, and four–volume into a single capacity relation.

1.2. Vacuum energy as a thin slice of Planck capacity

QTT reads the observed vacuum density as a thin “slice” of that same four–density, with a geometric factor and a small amplitude ε:

Equation

ρ_Λ = κ ε (ℏ c)/(4π ℓ_P⁴), κ = (1)/(3).

Equivalently, in terms of the Planck density ,

Equation

(ρ_Λ)/(ρ_P) = (κ ε)/(4π) = (ε)/(12π).

So the notorious suppression is encoded as a dimensionless weight multiplying a single geometric normalisation.

1.3. FRW consistency fixes ε (no tuning)

Matching this QTT vacuum density to the FRW dark–energy density fixes ε in terms of the de Sitter Hubble rate and the Planck time :

Equation

ε = (3)/(2κ)(H_Λ t_P)², (ρ_Λ)/(ρ_P) = (3)/(8π)(H_Λ t_P)².

Once are fixed, is not a free parameter: it is determined by the tiny ratio .

1.4. Cosmological constant in Planck units

The same match yields the cosmological constant in Planck units:

Equation

Λ = (8π G)/(c⁴) ρ_Λ = (2κ ε)/(ℓ_P²) = (2κ ε)/(c² t_P²) = (3H_Λ²)/(c²).

In QTT, “dark energy” is therefore vacuum capacity of Planck four–cells with a small amplitude ε fixed by cosmic expansion, not a separate dark fluid.

2. Dark matter → endurance gravity, MOND scale, and renewal dust

2.1. Gravity from endurance: Newtonian sector

From the Law of Endurance, each rest mass M consumes space quanta at rate

Equation

(dN_SQ)/(dT) = (M)/(tilde m) (1)/(t̃), V_SQ = 4π ℓ̃³.

This defines a four–volume sink rate

Equation

(dV^(4)_rm sink)/(dT) = (M)/(tilde m) (1)/(t̃) (4π ℓ̃⁴).

QTT interprets this as an endurance current . Its divergence is proportional to the mass density , and the Newtonian gravitational field is identified as

Equation

g = (c)/(ℓ̃) J_end.

In the continuum limit this yields

Equation

∇· g = -4π G ρ, G = (ℓ̃² c³)/(ℏ).

So QTT reproduces standard Newtonian gravity, but expresses G purely in terms of tick/step quantities .

2.2. MOND–like acceleration scale from the two clocks

The same two–clock geometry that sets the cosmic expansion also yields a natural low–acceleration scale. QTT predicts a MOND–like acceleration parameter:

Equation

a_0(z) = (c H(z))/(2π).

At , matches the empirical MOND acceleration scale that governs galaxy rotation curves and the radial acceleration relation.

Interpretation:

• No new particle species is introduced at galactic scales.
• Instead, two–clock kinematics implies that when , the effective relation between baryonic mass and acceleration crosses over from Newtonian to a MOND–like regime driven by the global Hubble rate.

This already replaces a large fraction of what ΛCDM attributes to cold dark matter.

2.3. Renewal dust as the remaining “dark matter”

QTT still allows an extra gravitational component, but it is not a new Standard Model–coupled particle. It is a purely gravitational renewal dust sourced by the endurance mechanism.

• Its stress–energy tensor is that of pressureless dust:

Equation

T^μν_rm RD = ρ_rm RD u^μ u^ν

It has no direct interaction with Standard Model fields:

Equation

mathcal L^int_RD = 0

i.e. it only gravitates.

The full Einstein equation in QTT then reads schematically:

Equation

G_μν + Λ g_μν = (8π G)/(c⁴)(T^SM_μν + T^RD_μν).

Here Λ and G are given by the QTT vacuum and endurance relations above. Dark matter is replaced by:

1. a low–acceleration modification
   Equation

   

   a_0(z) = cH(z)/(2π)

   from the two clocks, and

2. a non–SM interacting, purely gravitational renewal dust component originating from endurance flow, not a new WIMP/axion sector.

3. Time–plane tilt: geometric age gap and “dark energy” effects

QTT also rewrites part of dark–energy phenomenology as a geometric effect of the time–plane tilt between the Absolute Clock T and the laboratory clock tau:

• Two–clock relation:
  Equation

  

  dtau = mathcal N(x,v) dT.
• In cosmology, the misalignment angle between the lab time axis and the absolute time plane drifts with scale factor a as matter and vacuum content evolve.
• This leads to a projection factor between lab age and absolute age :

Equation

tau_0 ≃ (t_0)/(cosθ_rm eff).

Part of what looks like a “dark energy age tension” is therefore reinterpreted as geometry of the time plane, not exotic physics.

4. Boxed “dark sector replacement” summary

For quick reference, the core QTT replacement of the dark sector can be summarised in a single multi–line boxed relation:

Equation

textbfVacuum law:& ρ_Λ = κ ε (ℏ c)/(4πℓ_P⁴), ε = (3)/(2κ)(H_Λ t_P)², [0.4em] & Λ = (8π G)/(c⁴)ρ_Λ = (2κε)/(ℓ_P²) = (3H_Λ²)/(c²). [0.7em] textbfGravity from endurance:& ∇· g = -4π Gρ, G = (ℓ̃² c³)/(ℏ), [0.4em] & (dV^(4)_rm sink)/(dT) = (M)/(tilde m)(1)/(t̃) (4πℓ̃⁴). [0.7em] textbfMOND scale from two clocks:& a_0(z) = (c H(z))/(2π). [0.7em] textbfRenewal dust:& T^μν_rm RD = ρ_rm RDu^μ u^ν, mathcal L^int_RD = 0, [0.4em] & G_μν + Λ g_μν = (8π G)/(c⁴)(T^SM_μν+T^RD_μν).

5. Concrete tests against ΛCDM

QTT’s dark–sector replacement is falsifiable. Some sharp tests are:

1. Vacuum law test. Measure and (from SN Ia, BAO, CMB). QTT predicts

Equation

(ρ_Λ)/(ρ_P) = (3)/(8π)(H_Λ t_P)²

with no free parameter. Any robust disagreement falsifies the QTT vacuum law. MOND scale evolution. QTT predicts

Equation

a_0(z) = (c H(z))/(2π).

Test with high–redshift rotation curves and lensing: does the characteristic acceleration in the radial acceleration relation track H(z) this way? Renewal dust non–interactions. Renewal dust has with the Standard Model. Direct detection should keep seeing nothing; any positive dark–SM coupling at the expected densities contradicts QTT. Age–Hubble relations. The time–plane tilt implies specific age–Hubble identities (e.g. in the T–ledger) plus a geometric enhancement of absolute age over lab age. Compare precision stellar–chronometer ages with Hubble–rate determinations. Structure formation. N–body simulations with baryons + renewal dust + the modification must reproduce the matter power spectrum and CMB lensing without cold dark matter. Systematic mismatch at linear scales would challenge the QTT picture.

In short, QTT does not hide new particles in the dark; it rewires the dark sector into vacuum capacity, endurance–driven gravity, two–clock kinematics, and renewal dust—all governed by the same Planck–scale capacity laws that control the rest of the theory.