Cosmic Origins, Inflation, Dark Energy, and the Hubble Tension: A Single Fabric Account of the Universe

Temporal Congestion Mechanics (TCM) treats space as a physical medium — the fabric — governed by one master equation with ten anchored inputs. No additional field or parameter is introduced for cosmology. The universe began at the fabric’s structural maximum, n = n_H = √e, everywhere — bounded, finite, uniquely derived. Its relaxation is the Big Rebound: no singularity, no inflaton field, and no horizon or flatness problem requiring a solution. Every observable feature of cosmic history follows from the continuous relaxation of n from n_H back toward 1, governed by a single partial differential equation acting on a single field. Principal derived results (zero free parameters): • Hubble constant: H₀ = 72.97 km/s/Mpc (SH0ES distance-ladder measurement 73.04 ± 1.04 km/s/Mpc; 0.1%) • Dark energy density: ρ_Λ = 2/3ρ₀ (supernova magnitude–redshift record across 1,580 objects; sub-0.12%) • Matter fraction: Ω_m = 1/3 (0.04σ from the pipeline-extracted 0.334 ± 0.018) • Equation of state: w = −0.9999993, constant, w ≥ −1; no phantom crossing possible • CMB temperature: 2.7247 K derived (measured 2.7255 K; 0.03%) • Helium abundance: Y_p = 0.2458 (0.15σ from measured 0.2453 ± 0.0034) • First CMB acoustic peak: ℓ₁ = 220.5 derived analytically (measured 220.6); acoustic scale ℓ_A = 301.7, sound horizon r_s = 136.46 Mpc, comoving distance χ_* = 13,107 Mpc • Acoustic ruler: r_s = 140.2 Mpc from the three-mode compression-wave background • Matter–radiation equality: 1+z_eq = 4243 from measured pion kinematics (f_tot = 0.692, z_dep = 4.4 × 10⁷) • Spectral index: n_s = 1 from the ceiling structure; tensor-to-scalar ratio r = 0 • Seed amplitude — fully derived: δ_H = α_J²/√π = 3.004 × 10⁻⁵ against the sky’s anchored 3 × 10⁻⁵ (+0.15%). The pair-circuit computation derives both faces of the identity in six steps — winding conservation forces a two-vertex circuit carrying α_J²; the ceiling’s vanished knee enforces a self-similar, parameter-free population; Gaussian half-line smearing supplies √π; assembling these gives δu = α_J²/(4√π) = 7.511 × 10⁻⁶, lifted to the matter face by the exact fourfold transfer. Both kill conditions are met, the three coefficient readings adjudicated against printed alternatives. No dark matter, inflaton, or extra neutrino component is introduced. The Hubble tension is dissolved structurally: H₀ = 72.97 km/s/Mpc from the capacity density alone; CMB-inferred values reflecting uniform-model fits to a heterogeneous fabric. Falsification is explicit: an evolving equation of state, phantom dark energy (w < −1), primordial gravitational waves at r ~ 10⁻², or a detected dark matter particle each refute the account. The seed amplitude derivation adds a two-sided fence: a sharpened large-angle normalisation away from 3.004 × 10⁻⁵ kills the pair-circuit channel; any confirmed primordial non-Gaussianity beyond the α_J²-suppressed level kills it independently. The framework introduces no new parameters for cosmology. The same ten anchored inputs that produce gravitational, galactic, and particle-physics predictions in companion papers produce these cosmological derivations. The structural pattern across the framework is cross-domain consistency: one mechanism, one PDE, observables matching across all domains without adjustment.