Randomized trial derives discrete Friedmann equations for cosmological models, indicating further developments in understanding cosmic phenomena.
In Phase 1, we formalized the TRUE cosmological lattice, rewrote Einstein's equations in finite differences, and showed that the Big Bang singularity is replaced by a finite maximum density ρₘₐₓ = ρPlanck · γ_0. The present publication derives the discrete Friedmann equations on the TRUE lattice, starting from the discretized FLRW metric. We obtain finite-difference equations for the scale factor a(t), with a minimal temporal step h_0 and a natural cutoff at the TRUE Planck scale. We solve these equations in the radiation-dominated, matter-dominated, and cosmological-constant-dominated regimes. We show that the scale factor is finite at t = 0, with an initial value a(0) = aₘᵢₙ linked to γ_0. The solutions tend to the classical Friedmann solutions at large scales but exhibit predictive deviations at Planckian times. The condition k = +1 at the initial instant is derived as a logical consequence of the TRUE bound on density. A Von Neumann stability analysis demonstrates the stability of the scheme and the role of γ_0 as a natural filter on spurious modes. The relation between H_0ˡᵒᶜ and H_0ᶜᵒˢᵐᵒ is formulated with a geometric transfer factor τ, whose value will be constrained by data in Phase 3. We discuss implications for inflation, the Hubble tension, and primordial cosmology.
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Michel Febba (2026) studied this question.
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