a₀ Evolving: High-Redshift Galaxy Masses
Recent observations by the James Webb Space Telescope (JWST) have identified a population of massive galaxies at redshifts z > 10 that present challenges for the standard ΛCDM framework of structure formation. MIT predicts that the MOND acceleration scale a₀ is not a universal constant but an epoch-dependent quantity scaling with the Hubble parameter H(z).
This scaling follows directly from the identification of a₀ as an edge mode (n = 1) referencing the evolving Hubble horizon. Under standard H(z) evolution, the prediction a₀(z=10) ≈ 20 × a₀(0) implies enhanced effective gravitational binding during early galaxy assembly, accelerating structure formation without requiring modifications to star formation efficiency. Critically, MIT predicts a₀ evolves while the cosmological constant Λ remains fixed, the inverse of standard assumptions. Both predictions are independently testable with future high-redshift observations.
time-stamped paper can be found here
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I. THE OBSERVATIONAL TENSION
Observations of high-redshift galaxies by Labbé et al. reveal stellar masses M⋆ ~ 10¹⁰ M☉ formed within ~600 Myr after the Big Bang. These masses approach or exceed the maximal baryon abundance permitted in standard dark matter halos under ΛCDM, creating what has been termed the "impossibly early galaxy" problem. Resolving this tension within standard physics appears to require star formation efficiencies ε_SF exceeding unity, a physical impossibility suggesting either systematic observational errors or incomplete theoretical understanding.
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II. EPOCH-DEPENDENT ACCELERATION SCALE
Standard Modified Newtonian Dynamics (MOND) treats the acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s² as a fundamental constant. However, the observed coincidence a₀ ≈ cH₀ suggests a connection to horizon physics. This coincidence is dimensionally consistent: both a₀ and cH have units of acceleration.
Within MIT, observables scale from Planck units according to:
A/A_P = C(α) × Ω_ref^{−n/2}
where n is the dimensional index, C(α) is the phase coefficient at sampling position α, and Ω_ref is the relevant scale hierarchy. For acceleration, A_P = c/t_P = c²/ℓ_P ≈ 5.6 × 10⁵¹ m/s².
Edge modes (n = 1) reference the Hubble horizon:
Ω_H = (R_H/ℓ_P)²
Since R_H = c/H, we have Ω_H ∝ H⁻². Therefore:
a₀ ∝ Ω_H^{−1/2} ∝ H
Assumption: The phase coefficient C(α) remains constant across epochs. Within MIT, stable modes occupy Fibonacci-ratio domain fractions (α = F_n/120) due to non-resonance with the half-integer mode spectrum. These stability wells are topological features, motivating epoch-independence. This assumption is load-bearing for the quantitative prediction.
The resulting scaling relation is:
a₀(z) = a₀(0) × H(z)/H₀
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III. QUANTITATIVE ESTIMATE AT z = 10
For a standard flat cosmology with Ω_m ≈ 0.3 and Ω_Λ ≈ 0.7, the Hubble parameter evolves as:
H(z)/H₀ = √[Ω_m(1 + z)³ + Ω_Λ]
Note: We adopt standard cosmological H(z) evolution as a baseline for observational testing. MIT-consistent temporal evolution from the standing wave structure Ψ(t) = cos(t/2) is a subject for future work; deviations would constitute an additional testable prediction.
At z = 10: (1 + z)³ = 1331, giving Ω_m(1 + z)³ + Ω_Λ = 0.3(1331) + 0.7 ≈ 400. Thus:
H(z=10)/H₀ = √400 = 20
Applying the scaling:
a₀(z=10) ≈ 20 × a₀(0) ≈ 2.4 × 10⁻⁹ m/s²
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IV. IMPLICATIONS FOR STRUCTURE FORMATION
In the deep-MOND regime (g ≪ a₀), effective gravitational acceleration scales as g_eff ∝ √(g_N × a₀). Comparing epoch-dependent a₀ to the standard constant-a₀ assumption:
g_eff(z=10) / g_eff(standard) = √[a₀(z=10)/a₀(0)] = √20 ≈ 4.5
This factor of ~4.5 enhancement in effective gravitational binding significantly alters collapse dynamics. Since free-fall timescale scales as t_ff ∝ 1/√g, structures at z = 10 could collapse approximately 2.1× faster than standard MOND would predict.
For the Labbé et al. observations requiring ε_SF > 1 under standard assumptions, faster collapse dynamics would reduce the implied efficiency, potentially bringing it within the physically permitted range. The precise mapping from t_ff to ε_SF depends on feedback physics and would require hydrodynamic simulations with evolving a₀.
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V. CONTRASTING PREDICTIONS: a₀ vs. Λ
MIT's dimensional hierarchy makes a sharp distinction between edge modes (n = 1) and surface modes (n = 2):
a₀ (acceleration) ... n = 1 ... Ω_ref = Ω_H (evolves) ..... Prediction: Scales with H(z)
Λ (cosmo. const.) ... n = 2 ... Ω_ref = Ω_Λ (fixed) ...... Prediction: Constant across epochs
Here R_Λ = √(3/Λ) is the de Sitter radius, fixed by the topology. This represents an inversion of standard assumptions, where Λ is often treated as potentially evolving (dark energy equation of state w ≠ −1) while a₀ is assumed constant. Observations of both quantities at high redshift provide independent, complementary tests of the framework.
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VI. FALSIFICATION CRITERIA
MIT makes distinct predictions regarding the evolution of galactic dynamics:
Primary prediction: Rotation curve analyses of galaxies at intermediate redshifts (z > 2) should yield recovered a₀ values larger than the local value, scaling approximately as H(z)/H₀. At z = 2, this predicts a₀(z=2) ≈ 3 × a₀(0).
Secondary prediction: The cosmological constant Λ, measured via Type Ia supernovae or BAO at high redshift, should remain constant within observational uncertainty.
Falsification: If observations at z > 2 constrain a₀(z)/a₀(0) to unity at 2σ, the prediction is falsified. Similarly, if Λ is observed to evolve while a₀ remains constant, MIT's dimensional hierarchy requires revision.
These predictions distinguish MIT from both standard MOND (constant a₀) and ΛCDM (no acceleration threshold).
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REFERENCES
1. Labbé, I. et al. (2023). A population of red candidate massive galaxies ~600 Myr after the Big Bang. Nature 616, 266-269. DOI: 10.1038/s41586-023-05786-2
2. Milgrom, M. (1983). A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365.
3. McGaugh, S. S., Lelli, F., & Schombert, J. M. (2016). Radial Acceleration Relation in Rotationally Supported Galaxies. Phys. Rev. Lett. 117, 201101.
4. Shatto, B. (2025). Mode Identity Theory: Modal Realization on Nested Topology. DOI: 10.5281/zenodo.18064856
