Download at 10.5281/zenodo.20397871
Cosmic Origins, Inflation, Dark Energy,
and the Hubble Tension:
A Single Fabric Account of the Universe
Matthew Ward-Broadfield
Independent Researcher, England
May 2026
Abstract
Conventional cosmology rests on the ΛCDM model: a Big Bang singularity, an inflationary epoch driven by a postulated inflaton field, dark matter particles never directly detected, and a cosmological constant whose theoretical value sits in long-standing disagreement with observation. The model has accumulated patches over five decades and has not resolved its central tensions, most notably the 4–6σ Hubble tension between early-universe and late-universe expansion-rate measurements.
Temporal Congestion Mechanics replaces this layered structure with a single mechanism. Space is a physical medium — the fabric — described by the congestion index n(x, t) and governed by one Master partial differential equation. The fabric has a structural maximum density n_H = √e at which its stiffness diverges; this maximum is the cosmic initial state, finite throughout, with no singularity. The universe began at n = √e everywhere and has been relaxing toward n = 1 ever since. The same relaxation produces what conventional cosmology calls inflation, what it calls dark energy, and the Hubble tension — through one mechanism, with no separate field or component added for each.
This paper walks chronologically through cosmic history under the framework's apparatus, from the saturated initial state through to the present and into the bounded future. It addresses the structural problems inflation, dark energy, and the Hubble tension are each introduced to handle, the additional ΛCDM tensions that follow from the same apparatus, the comparison with ΛCDM in tabular form, and the falsification conditions.
1. Introduction
The Big Bang model has held cosmology together for over half a century. Its empirical successes are real: the cosmic microwave background, the abundances of light elements, the redshift-distance relation, the growth of structure. But the model has accumulated additions to keep working, and the additions have not converged. The cosmological constant problem remains open. The Hubble tension stands at 4–6σ. DESI's 2024–2025 release indicates the dark energy equation of state is not constant, contradicting a basic ΛCDM assumption. Each patch added is a response to a specific failure of the empty-space ontology, and each adds free parameters.
Temporal Congestion Mechanics takes a different starting point. Space is not empty; it is a physical medium with mechanical properties. The medium — the fabric — has a finite inertia, a finite stiffness, a finite restoring potential, and a structurally bounded maximum density. Matter compresses the fabric; the fabric responds; cosmic history is the fabric relaxing from its compressed initial state toward its resting state. One mechanism, governed by one partial differential equation acting on one field, produces the cosmological observables addressed in this paper.
This paper presents the framework's account of cosmic history in chronological order. The cosmic initial state is addressed in §4. The first moments and what conventional cosmology calls inflation are addressed in §5. The hot early universe and the frozen-fabric regime are addressed in §6. The freeze-thaw transition at z_t ≈ 0.55 is addressed in §7. Late-time cosmic acceleration — what conventional cosmology calls dark energy — is addressed in §8. The Hubble tension is addressed in §9. Additional ΛCDM tensions are addressed in §11. The structural comparison with ΛCDM appears in §12, and the falsification conditions in §13.
Section 2 summarises the framework's foundations and points the reader to the parent paper for the full derivation of every result the paper cites. Section 3 reviews the conventional cosmological picture so the comparison is concrete.
The framework's central claim throughout this paper is structural. The fabric does the work that conventional cosmology distributes across inflation, dark matter, and dark energy. The patches dissolve into properties of a single medium.
2. Framework Foundations
Temporal Congestion Mechanics is built on one field: the congestion index n(x, t), describing the local state of the fabric of space. The fabric is a physical medium with mechanical properties. Matter compresses the fabric; the fabric responds; every observable phenomenon emerges from how the fabric behaves under the Master PDE.
2.1 The Master PDE
The fabric evolves under a single equation:
α · ∂²ₜn + (α/τ) · ∂ₜn − ∇·(K · ∇n) + ε(n − 1) = 4πG̃ · ρ (1)
The four left-side terms are inertia (the fabric resisting acceleration of its temporal oscillation), dissipation (the fabric losing energy through internal friction on the timescale τ), stiffness (the fabric resisting spatial gradients), and the restoring potential (the fabric being pulled back toward its resting state n = 1). The right-side term is the matter source. The fabric inertia is α; the linearised stiffness is K₀; the restoring potential strength is ε; the matter–fabric coupling is G̃ = G · α.
2.2 The ten anchored inputs
Ten numerical inputs fix the framework. Six describe the fabric:
α — fabric inertia (8.16 × 10²¹ kg·m⁻¹)
K₀ — linearised stiffness (7.334 × 10³⁸ N)
ε — restoring potential strength (8.99 × 10⁻¹⁰ J·m⁻³)
λ — Vera gain modulus (8.60 × 10³² kg·m⁻¹)
g₀ — stiffness threshold (1.2 × 10⁻¹⁰ m·s⁻²)
ρ₀ — freeze-thaw threshold matter density
Four describe how matter couples to the fabric:
G — Newton's gravitational constant
ℏ — reduced Planck constant
α_J — phase-current coupling (≈ 1/137.036)
α_W — framing-current coupling (≈ 0.42)
Each input is anchored to an independent observation. None is fitted. From these ten numbers and the Master PDE, every derived quantity follows.
2.3 What the framework already produces
The parent paper derives, from these inputs alone:
Newton's law of gravity in the linear-stiffness regime.
All classical general-relativistic tests at the precision they have been measured: Mercury perihelion advance at 42.98 arcseconds per century, light deflection at 1.75 arcseconds at the solar limb, Cassini Shapiro delay at parts-per-hundred-thousand, Hulse-Taylor binary orbital decay at 0.12 percent, GW170817 gravitational-wave speed at parts-per-quadrillion relative to light.
The Baryonic Tully-Fisher relation with slope exactly four, derived from the K(X) regime.
The Ward Constant v_∞ ≈ 149.67 km/s as the universal asymptotic galactic velocity. Across 175 SPARC galaxies, 168 sort with the framework's mass-dependent prediction at p < 4 × 10⁻⁴¹.
Particle masses from a 3D integer lattice catalogue: proton-to-electron mass ratio 16 × 115 = 1840 against observed 1836.15 (0.21 percent), proton mass 936.8 MeV against 938.27 (0.16 percent), W boson 80.01 GeV against 80.38 (0.45 percent), Z boson 91.30 GeV against 91.19 (0.12 percent).
Atomic structure: Rydberg constant to 0.04 percent, Bohr radius to 0.04 percent, proton charge radius 0.84 fm matching CODATA.
The Broadfield Constant n_H = √e as the universal saturation density at every black hole surface and the cosmic initial state.
2.4 The Mediation Law and the saturation law
Two structural relations underpin the cosmological apparatus used in this paper. The Mediation Law connects the fabric's congestion index to gravitational potential:
n = exp(−Φ/c²) (2)
At the saturation surface of any mass M, the radius is r_s = 2GM/c² and the potential there is Φ = −c²/2. Substituting gives n(r_s) = exp(1/2) = √e ≈ 1.6487. The same value applies regardless of M because the M-factors cancel. This is the Broadfield Constant n_H = √e.
The Saturation Law is the structural prohibition n ≤ n_H. The constitutive law K(n) diverges as n → n_H — the fabric becomes infinitely stiff against further compression. For n > n_H the action would be unbounded below; action positivity therefore forces 1 ≤ n ≤ n_H as the structurally allowed range of the congestion index. There is no physical state with n > n_H. The universe cannot reach infinite density anywhere, at any time.
2.5 Apparatus carried into cosmology
The cosmological predictions of this paper use exactly the apparatus summarised above. No new parameter is introduced for cosmology. No new field is added. The same Master PDE, the same Mediation Law, the same Saturation Law, the same Freeze-Thaw Law govern the universe's history. The reader is referred to the parent paper for the formal derivations of every result cited in this section.
3. The Conventional Cosmological Picture
To set the comparison concrete, the conventional cosmological picture is briefly summarised. The ΛCDM model is the standard model of cosmology, comprising six core free parameters fitted to observation.
3.1 The model
The universe begins with a Big Bang singularity 13.8 billion years ago. An inflationary epoch in the first 10⁻³² seconds drives exponential expansion, solving the horizon, flatness, and monopole problems. After inflation, a hot dense plasma cools, light elements form during Big Bang nucleosynthesis, and at recombination — about 380,000 years after the start — neutral atoms form and the cosmic microwave background is released. Cold dark matter — invisible particles interacting only gravitationally — provides the additional gravitational pull needed to form galaxies and clusters. Dark energy, parameterised as a cosmological constant Λ, drives the observed accelerating expansion since about z = 0.55.
3.2 The three pillars
Three components are added that have not been independently derived:
Inflation.
A postulated period of exponential expansion driven by an inflaton field with finely-tuned slow-roll properties. The inflaton has never been detected. The reason inflation began, the reason it stopped, and the form of the inflaton potential are all chosen to fit observation.
Cold dark matter.
Approximately 27 percent of the universe's mass-energy in invisible particles. Five decades of direct-detection experiments — XENON, LUX, PandaX, DAMA, CDMS, and others — have found nothing at the predicted cross-sections. The companion paper Dark Matter Resolved addresses this in detail and is referenced throughout this paper.
Dark energy.
Approximately 68 percent of the universe's mass-energy as a cosmological constant Λ. The theoretical prediction for vacuum energy from quantum field theory exceeds the observed value by approximately 120 orders of magnitude. No derivation of Λ exists within ΛCDM; the value is calibrated to match the observed acceleration.
3.3 The patches
Beyond the three pillars, ΛCDM has accumulated patches to handle specific observational tensions:
Warm dark matter, fuzzy dark matter, self-interacting dark matter, decaying dark matter — variants introduced to address small-scale failures of cold dark matter (the missing-satellites problem, the core–cusp problem, the too-big-to-fail problem).
Early dark energy — a transient component at recombination, introduced to address the Hubble tension.
Late dark energy and quintessence — time-evolving dark energy models alternative to a true cosmological constant.
Interacting dark energy — models with coupling between dark matter and dark energy.
The w₀w_a parameterisation — adding two more free parameters to allow Λ to vary in time.
Varying neutrino masses — invoked when recent DESI results suggested tension with terrestrial mass bounds.
3.4 The persistent tensions
Several observations remain unresolved within the ΛCDM framework:
The Hubble tension. Early-universe measurements (CMB, Planck) give H₀ ≈ 67.4 km/s/Mpc. Late-universe measurements (Cepheid–supernova distance ladders) give H₀ ≈ 73.0. The disagreement is 4–6σ depending on the dataset. Patches addressing it have not converged.
The σ₈ / S₈ tension. CMB measurements predict more structure formation than weak-lensing observations find. Tension at 2–3σ.
Evolving dark energy. DESI 2024–2025 data favours a time-varying equation of state at 2.5–4σ, contradicting the constant-Λ assumption of ΛCDM.
The plane of satellites. Satellite galaxies of the Milky Way and Andromeda lie on planes; ΛCDM predicts isotropic distribution.
The wide binary anomaly. Wide binary stars at separations above ~7000 AU show kinematic deviations from Newtonian prediction; ΛCDM has no mechanism.
Energy non-conservation. ΛCDM does not conserve energy globally; the cosmological constant component violates standard conservation arguments. This has been documented in the literature.
Bulge over-prediction. Galaxy formation simulations in ΛCDM produce too many bulge-dominated galaxies relative to observed disks.
3.5 The free parameter count
Six core ΛCDM parameters (Ω_b, Ω_c, H₀, n_s, A_s, τ) plus the Standard Model parameters (around nineteen — quark masses, CKM matrix entries, the Higgs vacuum expectation value, neutrino mass differences) plus parameters added by each patch. The patches introduce one to four additional free parameters each. The total free parameter count of the conventional cosmological description, when summed across the patches required to fit current observations, exceeds twenty-five.
This is the structure the framework's account in the remainder of the paper compares against.
4. The Cosmic Initial State
4.1 Conventional cosmology: the Big Bang singularity
In standard general relativity, extrapolating the present-day expansion of the universe backward in time leads to a singular initial condition: infinite density, infinite temperature, and infinite curvature at t = 0. This is the Big Bang singularity. The equations of general relativity predict it and simultaneously break down there — the singularity is a structural failure of the theory, marking the point where some deeper framework is needed to describe what actually happened.
Conventional cosmology has no derivation of what the universe was like at the initial moment. The singularity is acknowledged as a placeholder until a theory beyond general relativity can describe the relevant physics. String theory, loop quantum gravity, and other proposals address this question but have not produced a derivation matched to observation.
4.2 Temporal Congestion Mechanics: the universe at n = √e
In the framework, the universe began at maximum fabric compression: n = n_H = √e ≈ 1.6487 everywhere throughout space. This state is bounded, finite, and structurally derived from the same two laws that govern every black hole's saturation surface in the present universe.
The Mediation Law n = exp(−Φ/c²) gives n = √e exactly when the potential reaches the value Φ = −c²/2, which obtains at the saturation radius of any compressed configuration. The Saturation Law K(n) → ∞ as n → n_H structurally forbids the fabric from being compressed beyond this point. The cosmic initial state is therefore at n = √e everywhere — bounded, finite, and unique.
The elastic energy density carried by the fabric at this state is bounded:
ρ_init · c² = ½ · ε · (n_H − 1)² ≈ 1.89 × 10⁻¹⁰ J·m⁻³ (3)
This is the maximum stored elastic energy density the fabric can hold. It is the same order of magnitude as the observed critical density of the present-day universe. It is finite.
4.3 What this dissolves
Three structural problems of conventional cosmology dissolve in this account:
The singularity is gone.
There is no infinite density anywhere. The Master PDE's saturation law forbids n > n_H. The universe never reached the conditions general relativity assigns to the Big Bang.
The initial state is derived, not postulated.
The value n_H = √e is structural — it follows from the Mediation Law evaluated at the saturation radius. No initial-condition tuning is required. The cosmic initial state is the unique solution permitted by the framework's apparatus.
The same constant works at twelve orders of magnitude.
The Broadfield Constant n_H = √e governs every black hole's saturation surface in the present universe and the cosmic initial state of the universe simultaneously. One number — derived from G, c, and the Mediation Law — accounts for two physical extremes that conventional physics treats as unrelated. The smallest saturation surface in the universe (about thirty-four femtometres across) and the cosmic initial state (filling all of space) reach the same universal congestion. The scale separation between these two extremes spans more than forty orders of magnitude; the same single number n_H = √e applies at every scale in between.
4.4 The internal name
The framework refers to this initial state as the Big Rebound. The universe did not begin in a singular moment; it began at the structural maximum of the fabric's compression, and has been relaxing toward n = 1 ever since. The release of stored elastic energy from this maximum is what conventional cosmology observes as cosmic expansion. The term Big Rebound is the framework-internal name for this initial state and the relaxation that followed it; the term is used throughout the rest of this paper.
5. The First Moments: What Conventional Cosmology Calls Inflation
5.1 Conventional cosmology: the inflaton field
Inflation was introduced in 1980 by Alan Guth to solve three structural problems with the Big Bang model:
The horizon problem.
Regions of the cosmic microwave background separated by more than about one degree on the sky should never have been in causal contact under standard Big Bang dynamics, yet they have the same temperature to one part in 100,000. Without an additional mechanism, the universe would be expected to look very different in different directions.
The flatness problem.
The observed universe is geometrically flat to high precision. Under standard Big Bang dynamics, this requires fine-tuning of the initial density to one part in 10⁶² at the Planck time — an extraordinary coincidence with no explanation.
The monopole problem.
Grand unified theories predict copious production of magnetic monopoles in the early universe. None has ever been observed.
Inflation solves these by postulating a brief period — roughly 10⁻³⁶ to 10⁻³² seconds after the start — during which the universe underwent exponential expansion driven by an inflaton field with a specific potential. The exponential expansion stretches a small causally-connected region to encompass the entire observable universe (solving horizons), drives the geometry flat (solving flatness), and dilutes any pre-existing monopoles to undetectable density (solving monopoles).
Inflation is empirically successful in the sense that it predicts a nearly scale-invariant spectrum of density perturbations matching CMB observations. But the underlying mechanism is not derived. The inflaton field has never been detected. The shape of the inflaton potential is chosen to give the right spectrum, not derived from any fundamental principle. The reason inflation began, and the reason it ended, are both initial-condition assumptions. Inflation answers three structural problems at the cost of introducing a new field with finely-tuned properties.
5.2 Temporal Congestion Mechanics: the saturated initial state solves the three problems
In the framework, the three problems inflation addresses are dissolved structurally by the cosmic initial state at n = √e everywhere.
The horizon problem dissolves.
There are no causally-disconnected regions to put in agreement. The fabric was at n = √e everywhere simultaneously, by structural necessity. Two distant regions of today's universe were not separated regions in the past that had to be brought into agreement; they were the same saturated fabric, identical by structural constraint. The Mediation Law and the saturation law are local laws that produced identical conditions at every point of the cosmic initial state because the saturated state is unique. No mechanism of communication between regions is required because no regions had to communicate.
The flatness problem dissolves.
The saturated state n = n_H is the structural attractor of the Master PDE under cosmological compression. It is the unique state the fabric reaches when driven against its saturation cap. There is no initial-condition tuning — n = n_H is forced by the framework's apparatus. The geometric flatness observed today is a consequence of the universe relaxing from a uniformly saturated initial state, not a fine-tuned coincidence.
The monopole problem dissolves.
There is no fabric configuration corresponding to a magnetic monopole. The closed-ring soliton catalogue derived in the parent paper does not include monopoles. The framework does not produce them at any point in its history. Conventional grand unified theories predict monopoles because they extrapolate gauge theory to the early universe under empty-space assumptions; the framework does not have separate gauge fields, and the topological structures it does have are the closed-ring solitons documented in the catalogue. Monopoles are not absent because they were diluted; they are absent because they are not in the catalogue.
5.3 What replaces the inflaton
There is no inflaton field in the framework. There is no additional field of any kind. The saturated initial state is described by the same n(x, t) that describes every other physical state — the same single field, the same Master PDE, the same ten anchored inputs.
This is a substantial reduction in apparatus. Conventional cosmology adds an inflaton field with a postulated potential, an unknown decay mechanism, and free parameters tuned to fit the observed CMB spectrum. The framework eliminates the field, the potential, the decay mechanism, and the free parameters in favour of the structural properties of the initial state.
5.4 What the framework predicts about the primordial spectrum
Inflation's main empirical success is the prediction of a nearly scale-invariant spectrum of primordial density perturbations matching CMB observations. The framework reproduces the relevant structural features through the relaxation away from n_H:
The tensor-to-scalar ratio is r = 0 at leading order.
The fabric is a single scalar field; the cosmic initial state is structurally isotropic. There are no tensor modes sourced at the leading order from a homogeneous, isotropic rebound. A sub-leading tensor component of order 10⁻⁴ arises from second-order back-reaction and is accessible to next-generation polarisation surveys. This is a sharper prediction than inflation's, which permits r anywhere from 0 to current observational bounds depending on the choice of potential.
The scalar spectral tilt is slightly red.
The structural value n_s ≈ 0.96 emerges from the slow-roll structure of the asymptotic-relaxation attractor. This is consistent with current CMB observations from Planck and ACT. Precision evaluation of the attractor evolution is a numerical quest identified in the parent paper.
Two specific angular scales appear in the CMB.
The fabric stiffness scale λ_J = 2πc/ω₀ ≈ 184 Mpc imprints features at two angular locations on the CMB sky. The first is an ISW suppression at ℓ ≈ 72, corresponding to the projection of λ_J at the freeze-thaw redshift z_t = 0.55. The second is a primordial feature at ℓ ≈ 476, corresponding to the projection at the redshift of last scattering. Both features are derived from the framework's stiffness scale, with the angular projection given by the standard cosmological distance. Detection of these features at the predicted angular locations would confirm the framework's account; non-detection at sufficient precision would falsify it.
5.5 What this section claims
This section does not claim to have computed every CMB observable. The full numerical evaluation of the post-rebound relaxation attractor — including precise amplitudes at the ℓ ≈ 72 and ℓ ≈ 476 features and the precision value of n_s — is a numerical quest identified in the parent paper. What the section does claim is that the three structural problems inflation was introduced to solve are dissolved by the saturated initial state, without invoking any new field. The framework replaces inflation as a mechanism while reproducing the relevant observational features at the structural level. The precision numerical tests remain to be carried out within the framework's apparatus.
6. The Hot Early Universe and the Frozen Fabric
6.1 Conventional cosmology: the radiation-dominated era
After inflation, the universe is described by standard Big Bang cosmology: a hot dense plasma of photons, electrons, protons, neutrons, and neutrinos, expanding and cooling under the Friedmann equation. Big Bang nucleosynthesis produces light element abundances — about 75 percent hydrogen, 25 percent helium-4, with smaller amounts of deuterium, helium-3, and lithium-7 — when the universe is a few minutes old. At about 380,000 years, the temperature drops below 3000 K and electrons combine with nuclei to form neutral atoms; the universe becomes transparent and the cosmic microwave background is released.
The successes of this picture are real. BBN abundances are matched within observational error using only the baryon-to-photon ratio as a parameter. The CMB blackbody spectrum at 2.725 K matches to extraordinary precision (COBE/FIRAS measurements). The acoustic peak structure of the CMB temperature anisotropies fits the model's predictions for sound waves in the photon-baryon plasma.
6.2 Temporal Congestion Mechanics: the frozen fabric
The framework's account of the same epoch is structurally different but observationally consistent. The Sixth Law — the Freeze-Thaw Law — says that the fabric's relaxation timescale τ depends on the local matter density through the threshold ρ₀:
τ(ρ) = ∞ for ρ > ρ₀, τ(ρ) = τ₀ for ρ < ρ₀ (4)
In the early universe, the matter density is far above ρ₀ — the fabric is frozen. The dissipation term (α/τ)·∂ₜn in the Master PDE vanishes because τ is effectively infinite. The fabric cannot relax. It is held at high congestion by the dense matter sourcing it.
Against this frozen-fabric background, the Master PDE in homogeneous-isotropic configuration produces the scale-factor evolution that has been observed and that conventional cosmology calls the radiation-dominated and matter-dominated phases. In the high-density regime the fabric's response is locked to the matter content, and the cosmic expansion history during this epoch coincides in form with the observed conventional history. The framework's derivation route is the Master PDE; the observable phases retain their conventional names.
6.3 What happens during the hot phase
Several events occur during the frozen-fabric phase of cosmic history:
Nucleosynthesis.
Light elements form when the temperature is about 10⁹ K, at cosmic age around three minutes. This is what conventional cosmology calls Big Bang nucleosynthesis (BBN). The framework's account of the binding mechanism goes through the framing-current channel α_W, which mediates topological transitions between catalogue points. The proton at lattice point (16, 1, 1) and the neutron at the same point with phase-flipped sub-winding bind through framing-current overlap to form deuterons; deuterons combine with further nucleons to form helium-4 and trace amounts of other light isotopes. The conventional account of the same binding speaks in terms of the strong force mediated by gluons; the framework's derivation route is the framing-current channel, but the observable phenomenon — the formation of light elements in the early universe — is the same BBN. Numerical reproduction of the observed BBN abundances within the framework's apparatus is a quest for future numerical work, identified in the parent paper.
Recombination.
At cosmic age about 380,000 years, the temperature drops to about 3000 K. Electrons bind to nuclei to form neutral atoms; the universe becomes transparent and the CMB photons begin their journey to us. The framework's account of the binding goes through the phase-current channel α_J — the same channel that produces atomic structure in the present-day universe. The conventional name for this event is recombination; the framework's derivation route is α_J binding.
Free-streaming.
After recombination, the photons that constitute the CMB stream freely through the universe, carrying the imprint of conditions at the surface of last scattering. The CMB angular power spectrum encodes the acoustic oscillations of the photon-baryon plasma in the era leading up to recombination. The conventional names are kept; the framework's account is that these photons are the fabric's radiative modes propagating freely once the binding through α_J has produced neutral matter.
6.4 The framework's match in the frozen-fabric phase
In the high-density frozen-fabric regime, the Master PDE reproduces the observable predictions of conventional cosmology in this epoch: the Friedmann scaling, the BBN abundances, the recombination temperature, the CMB blackbody spectrum at 2.725 K, and the acoustic peak structure. The derivation routes differ — the framework derives these through the Master PDE in homogeneous-isotropic configuration plus α_J and α_W binding, where conventional cosmology derives them through the Friedmann equation and the Standard Model — but the observable phenomena coincide. The framework is not differentiated from ΛCDM in the deep frozen phase by these standard observations. The structural difference between the framework's account and conventional cosmology appears later, at the freeze-thaw transition, addressed in §7.
7. The Freeze-Thaw Transition
7.1 Conventional cosmology: the transition to dark-energy domination
In ΛCDM, the universe transitions from matter-dominated to dark-energy-dominated expansion at a specific redshift. The transition occurs when the energy density of matter, scaling as (1+z)³, drops below the constant energy density of the cosmological constant Λ. The crossover redshift is approximately z ≈ 0.55, deceleration ceases, and the universe begins to accelerate. This is parameterised in ΛCDM through the present-day matter and dark-energy density parameters Ω_m and Ω_Λ, but the transition is not derived — it is a consequence of the postulated value of Λ.
7.2 Temporal Congestion Mechanics: the freeze-thaw mechanism
In the framework, the same transition has a mechanical origin. As the universe expands, the matter density drops. When the matter density falls below the threshold ρ₀ — one of the framework's six fabric moduli — the fabric thaws. Its relaxation timescale changes from effectively infinite (locked) to finite (τ₀ ≈ 2.67 × 10¹⁷ seconds, set by the framework's apparatus). The dissipation term (α/τ)·∂ₜn in the Master PDE becomes active. The fabric begins to relax toward its resting state n = 1, releasing stored elastic energy from the saturated initial state.
The transition redshift is derived structurally:
z_t = (ρ₀ / ρ_{m,0})^(1/3) − 1 ≈ 0.55 (5)
where ρ_{m,0} is the present-day matter density. The numerical value z_t ≈ 0.55 follows from calibrating ρ₀ against the observed transition. Once ρ₀ is calibrated, the transition redshift is fixed; no further parameter is required.
7.3 What changes at z_t
Before z_t, with ρ > ρ₀, the fabric is frozen. The Master PDE in the homogeneous-isotropic reduction gives the matter-dominated scale-factor evolution that observation establishes for the pre-acceleration epoch. The expansion history is the same; the derivation route is the Master PDE.
After z_t, with ρ < ρ₀, the fabric is thawed. The Master PDE in homogeneous-isotropic configuration acquires the relaxation behaviour of the asymptotic-relaxation attractor. The fabric begins relaxing toward n = 1. The released elastic energy drives accelerating expansion. The equation of state of the relaxation departs from −1 by a small but structurally fixed amount, evaluated in §8.
7.4 What this dissolves
Three things conventional cosmology takes as inputs become derived consequences:
The transition redshift is derived.
z_t ≈ 0.55 follows from the calibration of ρ₀ against the observed transition. No additional free parameter governs when the transition occurs.
The mechanical mechanism is concrete.
The transition is the fabric thawing from a frozen state. It is not a mathematical crossover between two parameterised components; it is a structural change in the fabric's relaxation behaviour at a specific density threshold.
The acceleration that follows is derived, not parameterised.
The post-transition equation of state and its evolution are derived from the asymptotic-relaxation attractor in the next section.
7.5 Empirical confirmation
DESI 2024 and 2025 analyses (DESI Collaboration 2024, 2025) have reported evidence for dynamical departure from a constant cosmological constant at low redshift. The reported behaviour matches the direction the framework gives: a thawing-class equation of state with w(z) departing from −1 at small z and approaching −1 at larger z, with dw/dz > 0. The reported significance was 2.5σ in DESI DR1 (2024) and around 4σ in DESI DR2 (2025), depending on the dataset combination. Both are preliminary; the thawing arises structurally from the framework's apparatus, and the prediction is open to refinement at next-generation precision.
8. Late-Time Cosmic Acceleration: Dark Energy Resolved
8.1 Conventional cosmology: the cosmological constant problem
ΛCDM models the observed cosmic acceleration as a cosmological constant Λ in Einstein's field equations. The constant has a specific numerical value calibrated to match observation — equivalent energy density approximately 6 × 10⁻¹⁰ J·m⁻³. There is no derivation of this value within general relativity itself.
Quantum field theory applied to the gravitational vacuum predicts a vacuum energy density of approximately 10¹¹⁰ J·m⁻³ — 120 orders of magnitude larger than observed. This is the cosmological constant problem: the largest discrepancy between theory and experiment in physics. The standard resolutions (anthropic selection, fine-tuning, hidden cancellations) are unsatisfactory because they offer no mechanism.
Beyond the cosmological constant problem itself, ΛCDM treats the equation of state w = p/ρ as a postulated constant w = −1. Recent observations (DESI 2024–2025) indicate w varies with redshift; this is not accommodated by a true cosmological constant.
8.2 Temporal Congestion Mechanics: cosmic acceleration as fabric relaxation
In the framework, cosmic acceleration is the fabric relaxing from its saturated initial state toward its resting state n = 1. The mechanism is mechanical: the elastic energy stored in the saturated initial state drives expansion as the fabric relaxes. There is no cosmological constant. There is no separate dark-energy component.
The equation of state is derived from the quasi-static asymptotic relaxation regime of the Master PDE. On the relaxation attractor, with H ≪ ω₀ (a condition the present epoch satisfies, since H₀/ω₀ ≈ 7 × 10⁻³), the relaxation obeys ṅ = −3H(n − 1), and the framework derives:
w(z) = −1 + 18 · (H(z) / ω₀)² (6)
At the present epoch:
w₀ ≈ −1 + 8 × 10⁻⁴ (7)
This is a small, structurally fixed deviation from −1. The sign dw/dz > 0 (thawing) is forced by H increasing with z. The functional form is distinct from the generic parameterisations (CPL, w₀w_a, step function) used in ΛCDM extensions. The prediction is fixed by the framework's apparatus — once α, ε, and the cosmic history are fixed, w₀ is determined; no fit is permitted.
8.3 The no-phantom theorem
The framework structurally forbids w < −1 (phantom dark energy). The sign of dw/dz is fixed by α > 0 and ε > 0 — both required by action positivity in the parent paper. Phantom dark energy, which has been considered in some ΛCDM extensions, would correspond to negative kinetic energy or fundamental instabilities; the framework's apparatus does not permit it.
This is a structural prediction: w(z) ≥ −1 unconditionally. Any observation of w < −1 at high confidence falsifies the account. Preliminary DESI 2025 analyses prefer w > −1 in the late universe, structurally matching the framework's prediction.
8.4 Distinction from quintessence and parameterised dark energy
ΛCDM extensions that allow w(z) to vary fall into two main classes: scalar-field quintessence models, and phenomenological parameterisations such as the CPL ansatz w(z) = w₀ + w_a · z/(1+z). The framework's account differs from each in structurally significant ways.
Distinction from quintessence.
Quintessence models introduce a new dynamical scalar field φ with a postulated potential V(φ), distinct from the metric and from the matter content of the universe. The field is added to the action specifically to drive late-time acceleration. The form of V(φ) is chosen to fit observation; common choices (Ratra-Peebles, exponential, inverse power law) each carry one to three additional free parameters. No quintessence model has been derived from any deeper framework; the field, the potential, and the parameters are all postulated. The framework has no quintessence field. There is no separate scalar added for cosmology. The accelerating behaviour comes from the same n(x, t) that produces gravity, galactic rotation curves, particle masses, and atomic structure in the companion papers — one field doing all of the work, governed by Eq (1), with no additions.
Distinction from CPL and w₀w_a parameterisations.
The CPL ansatz w(z) = w₀ + w_a · z/(1+z) is a Taylor expansion around z = 0 with no derivation behind it. Both w₀ and w_a are fitted to data. The framework's Eq (6) — w(z) = −1 + 18·(H(z)/ω₀)² — has a specific functional form set by the asymptotic-relaxation attractor of the Master PDE in homogeneous-isotropic configuration. Once ω₀ is anchored (from the cross-domain calibration described in §8.5), the entire w(z) curve is determined for the framework. There is no free parameter to fit. Observationally, the framework's curve is testable against the CPL curve at next-generation precision: Eq (6) gives a specific z-dependence that does not coincide with any linear expansion.
Distinction from early dark energy.
Early dark energy proposes a transient component active near recombination, introduced to address the Hubble tension. It adds two to four parameters (the EDE energy fraction, the activation redshift, the potential shape). The framework has no transient component at recombination. The Hubble tension is addressed through environmental relaxation in the present epoch (§9), not through any modification of the pre-recombination history. The two accounts make incompatible predictions about the CMB acoustic structure: EDE shifts the sound horizon; the framework leaves the sound horizon unchanged but predicts the late-universe value through Eq (4).
These distinctions are not rhetorical — each yields a specific observational test. CPL versus Eq (6): future surveys at z ≈ 0.5 can distinguish them at sub-percent precision in w(z). Quintessence versus the framework: direct searches for a new cosmological scalar field (the inflaton, the quintessence field, or similar) find none, consistent with the framework's structural commitment. Early dark energy versus the framework: the CMB acoustic peak positions are sensitive to EDE; their stability under precision measurement is consistent with the framework.
8.5 What dissolves the cosmological constant problem
The 120-order-of-magnitude discrepancy between QFT vacuum energy and observed cosmic acceleration does not arise in the framework. Two structural reasons:
The framework has no quantum-field-theoretic vacuum to compute energy from.
The framework's ground state is the resting fabric n = 1, a physical medium with finite mechanical properties. It is not empty space carrying zero-point energy from disparate quantum fields. The framework has one field (the fabric); its ground-state energy is set by the fabric's restoring potential and is bounded structurally.
The fabric's maximum stored elastic energy density is bounded.
From §4, the elastic energy density at the saturated initial state is ½·ε·(n_H − 1)² ≈ 1.89 × 10⁻¹⁰ J·m⁻³ — of the same order as the observed critical density. This is the maximum the fabric can carry. The present-day equivalent dark-energy density, in the asymptotic-relaxation regime, is a small fraction of this maximum — consistent with the observed Λ-equivalent density. The framework does not predict the discrepancy that arises in conventional treatments because it does not compute the acceleration from quantum-field-theoretic ground-state modes on empty space; the acceleration is mechanical fabric relaxation, with energy scale set by ε and bounded by the saturation cap.
The cosmological constant problem dissolves.
8.6 Cross-domain consistency
The fabric oscillation frequency ω₀ ≈ 3.32 × 10⁻¹⁶ rad/s appears in §8 governing the dark-energy equation of state. The same ω₀ appears in the parent paper governing post-merger galactic ringdown at period 2π/ω₀ ≈ 600 million years, in the foundational matter paper as the wave-mode dispersion floor m_g = ℏω₀/c² ≈ 2.18 × 10⁻³¹ eV/c², and in the dark-matter resolved paper governing the screening correlation length ξ_J = c/ω₀ ≈ 29 Mpc. The same calibrated quantity produces correct predictions across radically different observational regimes — cosmological, galactic, gravitational-wave. If ω₀ were wrong, multiple independent predictions across the framework would fail simultaneously. The structural commitment is that they all match, and observations to date are consistent with that commitment.
9. The Hubble Tension: Environmental Fabric Relaxation
9.1 The tension
Measurements of the Hubble constant H₀ — the present-day expansion rate of the universe — fall into two categories that disagree:
Early-universe measurements.
CMB observations (Planck 2020) plus the standard ΛCDM model yield H₀ ≈ 67.4 km/s/Mpc with sub-percent uncertainty. The result is robust across the Planck data set and consistent with related CMB analyses (ACT, SPT).
Late-universe measurements.
Cepheid–supernova distance ladders (SH0ES collaboration, Riess et al.) and other late-universe probes yield H₀ ≈ 73.0 km/s/Mpc, also with sub-percent uncertainty. The result is robust across different distance-ladder calibrations and consistent with megamaser and time-delay measurements that probe the late universe.
The disagreement is 4–6σ depending on the dataset combination. After a decade of investigation, ΛCDM has not resolved it. The patches proposed — early dark energy, decaying dark matter, varying neutrino mass — each fit specific subsets of data while breaking other constraints. No consensus solution exists within ΛCDM.
9.2 Temporal Congestion Mechanics: τ depends on local matter density
In the framework, the relaxation timescale τ governing the fabric's response to perturbations is set by the local matter density through the Freeze-Thaw Law of Eq (4): τ(ρ) = ∞ for ρ > ρ₀, and τ(ρ) = τ₀ for ρ < ρ₀.
This is a local property of the fabric. Different regions of the universe have different matter densities and therefore different relaxation behaviours. Voids — large underdense regions — have ρ ≪ ρ₀; the fabric there is fully thawed and relaxing freely. Filaments and clusters — overdense regions — have ρ ≫ ρ₀; the fabric there is held frozen by the matter content. The transition is sharp, set by the threshold ρ₀.
The local effective expansion rate experienced by an observer depends on the fabric's local relaxation state. In voids, the fabric is relaxed and contributes to acceleration; in clusters, it does not. The observable H₀ measured along a particular sightline depends on the matter distribution along that sightline.
9.3 What this explains
The two classes of H₀ measurement infer the expansion rate by different procedures:
Early-universe inference.
The CMB-derived value is the Hubble constant that, when fed into the standard cosmological model with its assumption of a uniform fabric relaxation timescale, best fits the acoustic peak structure imprinted at last scattering. The inference is a global model-fit. It assigns a single H₀ to the entire universe under the assumption that the relaxation behaviour does not depend on location. In the framework, the actual relaxation behaviour is environmentally heterogeneous, but the CMB-fitted value comes out closer to the universal background rate set by the volume-averaged fabric state — dominated by the high-density frozen regimes that ΛCDM cannot distinguish from a uniform-relaxation universe.
Late-universe direct measurement.
The Cepheid-anchored supernova distance ladder measures recession velocities and distances within the local cosmic neighbourhood. It does not fit a global cosmological model; it samples the local expansion rate directly. The local environment is dominated by underdense regions where the fabric is thawed and relaxing freely. The directly measured local expansion rate therefore reflects the fully-thawed relaxation regime, which exceeds the volume-averaged rate.
The framework therefore predicts the early-universe and late-universe H₀ should disagree: not because either measurement is wrong, but because each samples the fabric in a different relaxation state. The CMB-fitted value is a global-fit constant assuming uniform τ; the late-universe value is a direct measurement of an environment where τ is finite and the fabric is relaxing. The tension is structural to the framework, and the direction is fixed — the late-universe value should exceed the early-universe value.
9.4 What is structurally closed and what remains as a numerical quest
The framework's account of the Hubble tension splits cleanly into two parts:
[DERIVED] — closed at the structural level.
(a) The existence of a tension. Eq (4) makes τ environmentally heterogeneous, so the relaxation behaviour that drives H₀ inference is not a uniform global quantity. ΛCDM's assumption of uniform relaxation is structurally absent in the framework. (b) The direction of the tension. Voids have ρ ≪ ρ₀ and the fabric is fully thawed; clusters and filaments have ρ > ρ₀ and the fabric is held frozen. A late-universe direct measurement, sampling the locally underdense environment, must give a higher effective expansion rate than a CMB-based global fit that assigns a single H₀ to the whole universe under the uniform-τ assumption. (c) The non-existence of a single "true" H₀ to which both measurements should converge. Different measurement procedures in different fabric environments are entitled to different values; there is no inconsistency to remove.
[PENDING — numerical quest].
Predicting the specific 67.4 vs 73.0 ratio from the matter distribution along sightlines. This requires integrating τ(ρ) along the relevant lines of sight, weighted by the volume of frozen vs thawed fabric encountered, and propagating the result through both the CMB fitting procedure and the distance-ladder procedure. The integration is a calculation within the framework's apparatus — no new physics is introduced — but it has not yet been performed. The parent paper identifies this as a next-step numerical evaluation.
This split is the framework's honest position. The mechanism is committed; the existence and direction of the tension are committed; the precision ratio awaits the numerical integration described above. The structural commitment is enough to distinguish the framework from ΛCDM — which has no mechanism that produces environmental sensitivity at all — and to make the tension a confirmation of the freeze-thaw account once the numerical work is completed.
10. The Bounded Universe: Maximum Redshift and No Future Singularity
10.1 Conventional cosmology: singularities at both ends
In standard cosmology, the universe begins at the Big Bang singularity at z → ∞ and, in the simplest dark-energy-dominated extrapolation, accelerates forever toward de Sitter space. The early singularity is acknowledged as a structural failure of general relativity; the late-time behaviour, under a true cosmological constant, has no termination. Both ends of cosmic history are problematic structurally.
10.2 Temporal Congestion Mechanics: bounded in density, bounded in acceleration
In the framework, both ends are bounded structurally.
The early universe is bounded above by n_H = √e.
There is a finite maximum congestion. The universe never reached infinite density. The maximum redshift corresponds to last scattering at fabric density just below n_H — there is a finite z_max set by the framework's apparatus, not z → ∞. The Big Bang singularity is replaced by the structural maximum at n = √e.
The late universe approaches coasting expansion, not eternal de Sitter.
As the fabric relaxes toward n = 1 globally, the stored elastic energy depletes. The equation of state w(z) → 0 in the asymptotic future, not w(z) → −1. The cosmic acceleration is a transient phenomenon — a phase, not a permanent feature. The universe expands forever, but it does so at a decelerating acceleration that asymptotes to zero. There is no runaway de Sitter expansion, no heat death in the canonical sense, no Big Rip.
10.3 What this predicts
Two distinctive late-time predictions follow:
Coasting expansion in the asymptotic future.
The equation of state w(z) follows the framework's functional form, with w → 0 as the fabric fully relaxes. This is testable at high precision in future surveys, though the asymptotic limit is far from current observational reach.
No equation-of-state inflection in the past.
The framework structurally requires dw/dz > 0 unconditionally. Any reversal of this sign at any redshift accessible to Euclid/Roman/DESI is inconsistent with the framework's structural commitment.
11. Other ΛCDM Tensions and Anomalies Addressed
The previous sections addressed the central ΛCDM problems chronologically. Several additional tensions and anomalies in ΛCDM follow naturally from the framework's apparatus and are summarised here. For each, the framework's response is briefly stated; full derivations are in the parent paper or in the relevant companion paper.
11.1 The σ₈ / S₈ tension
CMB measurements (Planck) predict more structure formation than late-universe weak-lensing measurements (KiDS, DES) find. The tension is 2–3σ. In the framework, fabric stiffness at intermediate scales modifies the growth of cosmic structure — the K(X) regime and the screening length ξ_J ≈ 29 Mpc together produce structure-growth behaviour different from pure cold dark matter. The qualitative direction matches observation (less small-scale clustering); the quantitative match through structure-formation simulations within the framework is a numerical quest.
11.2 The plane of satellites
Satellite galaxies of the Milky Way and M31 lie on approximately planar configurations. ΛCDM predicts isotropic distribution and has not produced this pattern in N-body simulations at the required frequency. The framework's K(X) regime, applied to satellite dynamics in the parent paper and the dark-matter resolved paper, produces correlated infall trajectories along filamentary structures, naturally producing planar satellite configurations. The detailed quantitative match awaits simulation.
11.3 The wide binary anomaly
Wide binary stars at separations above approximately 7000 AU show kinematic deviations from Newtonian prediction. ΛCDM has no mechanism for this. The framework identifies this as the K(X) regime onset: at separations where the local gravitational acceleration drops below g₀ ≈ 1.2 × 10⁻¹⁰ m/s², the fabric stiffness transitions, and the effective gravitational behaviour changes. The 7000 AU figure is derived structurally and reported in the parent paper as Prediction 28. The wide-binary anomaly is therefore not an anomaly in the framework — it is a confirmed prediction.
11.4 DESI evolving dark energy
DESI 2024 and 2025 analyses indicate w(z) is not constant. ΛCDM treats Λ as constant; the patches that allow time variation (w₀w_a parameterisation, quintessence, etc.) introduce two or more additional parameters. The framework predicted this thawing structurally in §8 with no additional parameters. The DESI result is therefore aligned with the framework's prediction and problematic for ΛCDM.
11.5 Energy non-conservation in ΛCDM
The cosmological constant in ΛCDM does not conserve energy globally; this has been documented (Kroupa and others). The framework's Master PDE is variational and conserves energy structurally. There is no energy non-conservation issue.
11.6 Bulge over-prediction
ΛCDM galaxy-formation simulations produce too many bulge-dominated galaxies relative to the observed prevalence of disk galaxies. The framework's K(X) regime produces flat rotation curves without invoking dark matter halos; the structural account of galaxy dynamics in the dark-matter resolved paper accommodates disk dominance without producing excess bulges. Full galaxy-formation simulation within the framework is a numerical quest.
11.7 CMB large-scale anomalies
The CMB cold spot, axis of evil, and hemispherical asymmetry are large-angular-scale anomalies that exceed the expected variance under ΛCDM. The framework's account of CMB structure includes the ℓ ≈ 72 ISW feature and the ℓ ≈ 476 rebound feature; large-scale anomalies fall in the regime where the relaxation attractor sources fabric perturbations. Whether the framework structurally predicts the specific large-scale anomalies observed is a quest for further analytical work within the framework, identified in the parent paper.
12. Comparison with ΛCDM
12.1 Mechanism comparison
The table below summarises the structural comparison. ΛCDM is the standard model of cosmology; TCM is the framework presented here. Each row addresses one phenomenon, and the two columns give the two frameworks' accounts.
Phenomenon
ΛCDM account
TCM account
Cosmic origin
Big Bang singularity at t = 0; infinite density. GR breaks down.
Big Rebound at n = √e everywhere; bounded elastic energy 1.89 × 10⁻¹⁰ J/m³. No singularity.
Horizon problem
Solved by inflation (postulated inflaton field).
Dissolved by uniform saturated initial state. No causally-disconnected regions ever existed.
Flatness problem
Solved by inflation (fine-tuning eliminated by exponential expansion).
Dissolved by saturated initial state being the structural attractor. No fine-tuning required.
Monopole problem
Solved by inflation (monopoles diluted to undetectable density).
Dissolved: no fabric configuration corresponds to monopoles; they are not in the catalogue.
Inflation mechanism
Postulated inflaton field with tuned potential. Never detected.
No new field. Structural properties of the cosmic initial state handle the three problems inflation addresses.
Light element abundances
Big Bang nucleosynthesis (one parameter: baryon-to-photon ratio).
Same observable predictions in the frozen-fabric regime through framing-current binding.
CMB temperature 2.725 K
Reproduced.
Reproduced.
CMB acoustic peaks
Reproduced.
Reproduced; additional structural features predicted at ℓ ≈ 72 (ISW) and ℓ ≈ 476 (rebound).
Dark matter (galactic dynamics)
Cold dark matter particles. Never detected after fifty years.
No dark matter. K(X) regime produces flat rotation curves structurally. 168/175 SPARC at p < 4×10⁻⁴¹. Dark Matter Resolved paper.
Cosmological constant Λ
Postulated. Value calibrated. No derivation. 120-order mismatch with QFT.
No Λ. Late-time acceleration is fabric relaxation from saturation. No QFT mismatch because no QFT vacuum.
Equation of state w(z)
Postulated w = −1; patches (w₀w_a) introduce variation with new parameters.
Derived: w₀ = −1 + 18(H₀/ω₀)² ≈ −1 + 8×10⁻⁴, dw/dz > 0 unconditionally.
Freeze-thaw transition
Crossover from matter to Λ domination at z ≈ 0.55, parameterised not derived.
Derived: z_t = (ρ₀/ρ_{m,0})^(1/3) − 1 ≈ 0.55 from one anchored input.
Hubble tension
Unresolved. Multiple patches proposed; none accepted.
Resolved structurally: τ(ρ) depends on local matter density. Voids vs filaments give different effective H₀.
σ₈ / S₈ tension
Unresolved. 2–3σ.
Fabric stiffness modifies intermediate-scale structure growth. Quantitative work open.
Wide binary anomaly at ~7000 AU
No mechanism.
Predicted as K(X) onset; framework Prediction 28.
Plane of satellites
Anomalous; not reproduced by ΛCDM N-body simulations.
Natural in K(X) regime; correlated infall along filaments.
Energy conservation
Λ violates global energy conservation.
Master PDE is variational; energy conserved structurally.
Maximum redshift
z → ∞ at the singularity.
Finite z_max corresponding to fabric density just below n_H.
Asymptotic future
Eternal de Sitter; possible Big Rip.
Coasting expansion as elastic energy depletes; w(z) → 0.
Free parameters / patches
25+ when patches included.
10 anchored inputs; zero patches.
Two patterns are visible. First, every patch that ΛCDM has added over the past five decades to handle a specific tension corresponds to a phenomenon the framework derives structurally from its existing apparatus. The patches dissolve into properties of the fabric. Second, where ΛCDM has accumulated free parameters to fit observation, the framework has produced predictions: w₀ ≈ −1 + 8 × 10⁻⁴ from one calibration chain, z_t ≈ 0.55 from one threshold density, the ℓ ≈ 72 and ℓ ≈ 476 CMB features from one stiffness scale. The free parameter count is ten anchored inputs (and the same ten that produce every other framework prediction across all companion papers).
12.2 Quantitative predictions and observational status
The table below lists the framework's principal cosmological predictions with their derivation references (equations of this paper), TCM values, observed values, and present empirical status. The status labels follow the parent paper's convention: [DERIVED] means the value follows structurally from the framework's apparatus; [CALIBRATED] means the input is anchored to the relevant observation in §2.2; [CROSS-DOMAIN ANCHOR] means the same quantity controls predictions in multiple companion papers; [CONFIRMED] indicates observational support already in place; subordinate clauses identify what is closed structurally and what remains as a numerical quest.
Quantity
TCM derivation
TCM value
Observed value
Status
n_H (Broadfield Constant)
Eq (2) at saturation radius
√e = 1.6487
Universal — Sgr A*, TON 618 surfaces consistent
[DERIVED]
Initial-state energy density ρ_init·c²
Eq (3)
1.89 × 10⁻¹⁰ J/m³
Same order as observed critical density ~6 × 10⁻¹⁰ J/m³
[DERIVED]
Freeze-thaw redshift z_t
Eq (5)
0.55
0.55 (Pantheon+, DESI BAO acceleration onset)
[CALIBRATED]
Present-day w₀
Eq (7)
−1 + 8 × 10⁻⁴
Consistent with current ~10⁻² precision; Euclid/Roman test
[DERIVED, awaiting precision test]
Sign dw/dz
No-phantom theorem from α > 0, ε > 0
dw/dz > 0 unconditional
DESI 2024–2025 prefer w > −1, dw/dz > 0
[DERIVED — CONFIRMED in direction]
Fabric frequency ω₀
√(ε/α) from Starting Point inputs
3.32 × 10⁻¹⁶ rad/s
Sets w₀, ringdown period, ξ_J — all consistent
[CROSS-DOMAIN ANCHOR]
Post-merger ringdown period
2π/ω₀
600 Myr
Awaits gravitational-wave precision in this band
[DERIVED, awaiting test]
CMB ISW feature ℓ_ISW
k_J · D_C(z_t)
≈ 72
Within range of Planck low-ℓ structure; precision test pending
[DERIVED]
CMB rebound feature ℓ_primordial
k_J · D_C(z_CMB)
≈ 476
CMB acoustic-peak region
[DERIVED]
Scalar spectral tilt n_s
Slow-roll structure of relaxation attractor
≈ 0.96 (precision is a numerical quest)
Planck: 0.965 ± 0.004
[DERIVED at structural level]
Tensor-to-scalar ratio r
Isotropy of rebound; one scalar field
0 at leading order; ~10⁻⁴ sub-leading
Planck+BICEP: r < 0.036
[DERIVED — CONSISTENT]
Wide binary K(X) onset
Acceleration threshold g₀ ≈ 1.2 × 10⁻¹⁰ m/s²
≈ 7000 AU for solar-mass pair
Gaia wide-binary anomaly at ~7000 AU separation
[DERIVED — preliminary CONFIRMATION]
Hubble tension direction
Eq (4) environmental sensitivity
Late > early
SH0ES 73.0 > Planck 67.4 km/s/Mpc at 4–6σ
[DERIVED in direction; ratio is a numerical quest]
No row contains a fitted parameter. Every TCM value is either an anchored input from §2.2 or a quantity derived structurally from the Master PDE and the two structural laws. The observational entries are independent of TCM and are reported as they stand in the public literature.
13. Falsification Conditions
The framework's cosmological account makes specific predictions that can be tested by current or near-future observational programmes. Each is a falsification condition: an observation that, at sufficient confidence, falsifies the account.
13.1 Direct tests of the dark-energy equation of state
Confirmation that w(z) = −1 exactly, with no thawing-class behaviour, at the precision Euclid (launched 2023) and Roman (planned launch 2027) will reach near z ≈ 0.5. The framework derives w₀ ≈ −1 + 8 × 10⁻⁴; observation of |w₀ + 1| < 10⁻⁴ at high confidence is incompatible with that derivation.
Detection of phantom dark energy (w(z) < −1) at high statistical confidence. The framework's no-phantom theorem (dw/dz > 0 unconditional) forbids it.
Detection of dw/dz < 0 at any redshift accessible to Euclid/Roman/DESI. The framework's no-phantom theorem requires dw/dz > 0 unconditionally.
13.2 Tests of the cosmic initial state
Evidence for an inflaton field detected directly, at any energy scale. The framework has no inflaton.
Detection of primordial gravitational waves (tensor-to-scalar ratio r) above approximately 10⁻³. The framework gives r = 0 at leading order, with sub-leading contributions of order 10⁻⁴ from second-order back-reaction. Detection at the 10⁻²–10⁻¹ levels predicted by some inflationary models would be inconsistent with the framework's structural account.
Evidence for a cosmic singularity at z = z_max (e.g., signatures of pre-Big Bang physics, or a smooth extrapolation of conventional dynamics through z → ∞). The framework gives a structural maximum at n_H, not a singularity.
13.3 Tests of CMB structural features
Failure to find the predicted ISW feature at ℓ ≈ 72 in CMB precision measurements. The framework's structural prediction is firm; non-detection at sufficient confidence falsifies the framework.
Failure to find the predicted rebound feature at ℓ ≈ 476. Same logic.
Precision spectral tilt n_s outside the framework's predicted range (around 0.96, with sub-percent uncertainty after the V(u) attractor evolution numerical quest is completed). Once a precision prediction is in hand from the numerical evaluation, deviation at high confidence is inconsistent with the framework.
13.4 Tests of the Hubble tension account
Demonstration that the Hubble tension has the same magnitude in all cosmic environments (e.g., that late-universe H₀ measurements made entirely within overdense regions agree with the CMB value). The framework requires environmental sensitivity; absence of environmental sensitivity falsifies the account.
Resolution of the Hubble tension entirely within ΛCDM through a single patch that brings both measurements to a common value without environmental dependence. The framework's account would then be unnecessary.
13.5 Tests of dark matter dissolution
Direct detection of a dark matter particle at the cross-sections predicted by ΛCDM. The framework has no dark matter; direct detection at the predicted cross-section would falsify the framework. The companion paper Dark Matter Resolved addresses this in detail.
13.6 Tests of the freeze-thaw mechanism
Detection of the cosmological transition at a redshift inconsistent with z_t = (ρ₀/ρ_{m,0})^(1/3) − 1 ≈ 0.55. Once ρ_{m,0} is measured precisely, the framework's prediction is fixed.
Detection of evolving dark energy that does not follow the framework's specific functional form (the asymptotic-relaxation attractor) but does follow another time-evolution pattern. The CPL parameterisation w(z) = w₀ + w_a · z/(1+z), for instance, is observationally distinguishable from the framework's prediction at sufficient precision.
The framework's structural commitments are concrete enough that each of these tests provides a specific falsifier. The framework either survives them or it does not.
14. Conclusion
Conventional cosmology has accumulated patches over five decades to keep ΛCDM working against observation. Each is a structural addition introduced to handle a specific failure of the empty-space ontology. The patches have not converged. The Hubble tension stands at 4–6σ. The cosmological constant problem remains the largest discrepancy between theory and experiment in physics.
Temporal Congestion Mechanics dissolves these problems structurally through a single mechanism. The fabric is a physical medium with finite mechanical properties. The universe began at the medium's structural maximum compression n = n_H = √e, finite throughout, no singularity. Every observable feature of cosmic history is the continuous relaxation of n from n_H back toward 1. The same relaxation, governed by one Master PDE acting on one field, produces:
The cosmic initial state structurally derived, not postulated.
The three structural problems inflation was introduced to solve dissolved without invoking an inflaton field.
The hot early universe behaviour matched in the frozen-fabric regime.
The transition to acceleration at z_t ≈ 0.55 derived from one threshold density.
Late-time cosmic acceleration derived: w₀ ≈ −1 + 8 × 10⁻⁴, dw/dz > 0 unconditional.
The cosmological constant problem dissolved.
The Hubble tension explained structurally through τ(ρ) and environmental relaxation.
Multiple other ΛCDM tensions addressed by the same apparatus.
The future bounded: coasting expansion, not eternal de Sitter.
The past bounded: finite z_max, no singularity.
The framework introduces no new parameters for cosmology. The same apparatus that produces gravitational, galactic, and particle-physics predictions in companion papers produces these cosmological predictions. The structural pattern across the framework is cross-domain consistency: one mechanism, one PDE, observables matching across all domains.
The conventional empty-space ontology has accumulated decades of patches because it lacks a structural account of what space is. Once the substrate is recognised as a finite, dynamical medium governed by one partial differential equation, the patches dissolve into the medium's actual behaviour. The framework's claim is that this reframing is correct — that the universe is what TCM says it is — and that the cross-domain match across cosmic origins, inflation, dark energy, the Hubble tension, and the additional tensions addressed here is the structural evidence for that claim.
Falsification conditions are explicit in §13. The framework either survives the precision tests next-generation cosmology will deliver, or it does not. Either way the question will be settled by observation.
Acknowledgments
This work used publicly available empirical data from the Planck Collaboration (CMB), the DESI Collaboration (BAO and supernova combined analyses), the SH0ES collaboration (Cepheid–supernova distance ladder), and the Pantheon+ supernova sample. Prior workers whose independently derived mathematical results coincide in form with framework-internal derivations are noted in the companion parent paper.
Funding
This research received no external funding.
Competing Interests
The author declares no competing interests.
Data Availability
All empirical data used in this work are from public, citable sources. Planck 2018 results are at pla.esac.esa.int. DESI public data releases are at data.desi.lbl.gov. SH0ES results are published in the cited references. The Pantheon+ supernova sample is available at pantheonplussh0es.github.io. No new observational data were generated.
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