Evolution of the Universe

From referenceability to the present cosmological state within MQ. The Frames mapping relates dimensionless configuration structure to realized cosmic quantities. The adopted geometry, realization and temporal normalization remain assumptions of the displayed construction; this overview is not a complete independently established cosmological evolution theory.

Illustrative ordering

The quantum epoch is pre-referenceable configuration structure. Its configuration domain is nonphysical, vectorless and dimensionless, with no intrinsic physical geometry, elapsed clock time or physical units. The cone, luminous seed and galaxies are conceptual illustrations; the pre-referenceable part is not a picture of literal physical space or a measured radius. Minimum realized closure marks the referenceability threshold and transition to the expansionary epoch. The expansionary epoch concerns realized geometry, expansion and mass realization. Stars, galaxies and large-scale structure emerge within the observable domain. Present-state relations distinguish observable and dark geometric domains. Ordering is illustrative and spacing is not a linear or logarithmic time scale.

Symbol definitions

The dimensionless MQ coefficient is theta_si. Its momentum realization p_si is distinct and has physical units kilogram metres per second. Fundamental mapped reference measures l_f, m_f and t_f have units metres, kilograms and seconds. The vacuum speed of light c is l_f divided by t_f and is in metres per second. Configuration representations do not thereby inherit physical units. A_U is realized System Frame age; R_U and D_U are the corresponding MQ universe-scale radius and diameter in metres. They are not automatically the conventional particle-horizon radius or observable-universe diameter. n_Tu is the dimensionless temporal count of A_U in t_f units. R_min is minimum realized closure radius under the adopted three-generator construction. Pi is the upright circle constant. In the radius and diameter relations theta_si is dimensionless, so age times c has length units. Momentum p_si belongs in the separate CMB-based age reconstruction. The si subscript is italic. Geometric-domain constants use upright capital Omega.

Minimum referenceable universe and epoch mapping

R_{min} = \sqrt{3} l_{f}

t_{ref} = 1 s

A_{ee} = A_{qe} {(2 θ_{si})}^{\frac{1}{3}}

A_{qe} = 363312.35 yr

A_{ee} = 678894.26 yr

The fixed reference t_ref is one second in this temporal normalization. The mapped quantum extent A_qe is t_ref times exp of square root of three times theta_si cubed divided by two. It equals 363312.3525(25) Julian years in the source representation; A_ee equals A_qe times cube root of two theta_si, giving 678894.2574(47) Julian years. They are two related epoch representations; their displayed comparison is not two physical clock readings within the configuration domain. The panel rounds their central values to two decimal places. A_qe does not assert intrinsic elapsed quantum-epoch time. Seconds and years belong to mapped realized descriptions.

Cosmic age and scale

n_{Tu} = \frac{A_{U}}{t_{f}}

R_{U} = A_{U} θ_{si} c

D_{U} = 2 θ_{si} A_{U} c

Mass-equivalent allocation

M_{tot} = n_{Tu} m_{f} \frac{θ_{si}^{3}}{2}

M_{acr} = \frac{θ_{si}^{3} m_{f}}{2 t_{f}}

M_tot is the assigned total mass equivalent, in kilograms, under the adopted count ratio. M_acr is its constant allocation rate per realized time, in kilograms per second. These are conditional relations of the stated MQ count and normalization model. This poster does not establish that material mass is produced at a measured constant rate or that radiation energy is conserved unchanged during expansion.

CMB temperature and cosmic age

T_{CMB} = \sqrt[4]{\frac{ρ_{CMB}}{a}}

T_{CMB} = 2.72548 (57) K

A_{U} = \sqrt[3]{\frac{3 p_{si} A_{ee}}{4 π a c l_{f} T_{CMB}^{4}}}

A_{U} = 13.7943 (38) Gyr

T_CMB is the physical measured cosmic microwave background temperature input, 2.72548(57) kelvin. Rho_CMB denotes radiation energy density in joules per cubic metre. The radiation constant a is 7.565733250 and further digits times ten to the minus sixteen joules per cubic metre per kelvin to the fourth power. The age reconstruction uses measured CMB temperature, the mapped expansionary extent A_ee, momentum p_si and the stated MQ reference relations, with the explicit one-second temporal convention in A_qe. It gives 13.7943(38) billion Julian years under those premises. This is a CMB-based age reconstruction rather than an independent prediction of the CMB temperature. Parentheses in source-derived values indicate conditional propagated standard uncertainty in final digits; unquantified model uncertainty is not assigned an experimentally established zero.

Geometric partitions

Ω_{obs} = \frac{4}{θ_{si}^{2} + 2}

= 31.6375838776 (41)%

Ω_{dk} = \frac{θ_{si}^{2} - 2}{θ_{si}^{2} + 2}

= 68.3624161224 (41)%

Ω_{vis} = \frac{2}{θ_{si} (θ_{si}^{2} + 2)}

= 4.8488348909 (10)%

Omega_obs, Omega_dk and Omega_vis are the observable, complementary dark and visible geometric referenceability-domain fractions. Their numerical values are shown in percent. Omega_vis is within Omega_obs, and Omega_obs plus Omega_dk equals one. These geometric constants are not automatically conventional fitted cosmological matter and dark-energy density parameters.

Cosmic expansion comparison rates

H_{sys} = \frac{π}{θ_{si} A_{U}}

= 68.259 (19)

km s^{-1} Mpc^{-1}

H_{int} = \frac{2 θ_{si} - π}{θ_{si} A_{U}}

= 73.508 (20)

km s^{-1} Mpc^{-1}

H_sys is the System Frame-resolved comparison frequency and H_int is the complementary configuration-resolved comparison frequency. Both physical frequencies are realized quantities, not a physical clock or expansion within the nonphysical configuration domain. A_U is in seconds in their symbolic expressions; their displayed numerical values are converted from inverse seconds to kilometres per second per megaparsec. The conversion uses one megaparsec equal to 3.08567758149 times ten to the nineteenth kilometres. Their shared input dependence is not independent observational evidence. No parameter fit is performed in this infographic. No equation numbers or visible material below the infographic are added.

Evolution of the Universe

From Referenceability to the Present Cosmological State

Measurement Quantization (MQ) approaches the evolution of the universe from a question more fundamental than how an already existing universe expands. It first asks what physical conditions are required for a universe to become referenceable at all.

MQ begins with one axiom, “measure is discrete.” From logical count relationships, the framework geometrically anchors an expanding frame of information whose physical realization describes a universe. Four measured inputs identify and normalize the realization considered here—the fine-structure constant, speed of light, electron mass, and Bohr radius. These serve different selection and normalization roles; they are not four statistically independent measurements. The speed of light is exact in SI, and the measured cosmic microwave background temperature separately selects the epoch.^[4]

This distinction changes the starting point of cosmology. The Internal Frame is the discrete configuration domain of logical count relationships. The Frames mapping realizes those relationships as continuous relational separations in the System Frame, where physical observables are defined. MQ therefore describes cosmic history through the realization of count structure, from the conditions for referenceability to its proposed present cosmological state. Mapping, closure, and realization requirements retain their stated roles in each derivation.^[1]^[4]

The resulting picture connects the fundamental measures, the frames of reference, the quantum epoch, mass accretion, the age and diameter of the universe, and the cosmological expansion rate within one count-based description.

The Origin of a Referenceable Universe

The origin treatment uses the Universe Initiation Theorem. Under its conservation, persistence, record, and mapping conditions, a localized open-boundary defect can coexist with a maximal referenceable domain. The defect obstructs extension of a valid realization to the entire configuration domain, while the referenceable domain satisfies its own closure conditions. This is an atemporal structural description; it does not place a clock or material space outside the first physical realization.^[1]

Let U be a referenceable domain and γ a contractible reference cycle within it. The mapping holonomy ℋ_M measures the mismatch in reference data after transport around the cycle. A necessary closure condition is

ℋ_M(γ) = 0. This condition applies to admissible contractible cycles in the valid domain. It does not require every noncontractible cycle or every cycle through a mapping defect to have zero holonomy.

For the defect criterion, let ω′ be a bounded candidate configuration region, A its update index, Φ_I(∂ω′, A) its boundary count flux, and 𝒟(ω′) its mapping-defect class; ∂ denotes the boundary. The criterion requires both nonzero boundary flux and nonzero holonomy on at least one contained reference cycle. The cycle in this test is not asserted to be an admissible contractible cycle in the valid domain.

𝒟 (ω') \neq \emptyset \Leftrightarrow Φ_{I} (\partial ω', A) \neq 0 \land \exists γ \subset ω' : ℋ_{M} (γ) \neq 0

The distinction is between a defect in the candidate configuration and consistent realization on the referenceable domain. Count transfer alone does not establish a universe. The theorem also requires persistence, a valid maximal mapping domain, and the closure-supporting structure described next.

Within the theorem’s orthogonal closure construction, three algebraically independent reference generators provide the minimal set. Let R_min be the minimum realized closure distance and l_f the fundamental measure of length. Assigning one length realization to each generator gives

R_{min} = \sqrt{3} l_{f}

The factor √3 comes from the norm of three independent unit-count directions. It does not assume a pre-existing Euclidean physical space. Within the stated realization conditions, the first referenceable scale is finite.^[1]

Physical Referenceability

This provides an important conceptual boundary. MQ does not claim that a smaller mathematical coordinate cannot be written. It states that physical referenceability begins only when the count structure satisfies the conditions required for realization. The distinction between mathematical extrapolation and physically realizable measure is central to the MQ account of cosmic origin.

From Initiation to Physical Measure

Once referenceability is established, evolution can be expressed through count. Alongside the length reference, the fundamental measures m_f and t_f supply the mass and time references. They are physical realizations of the underlying count relationships, rather than rods, clocks, or matter presupposed in the logical domain. The fundamental relation is l_fm_f = 2t_fp_si, where p_si is the momentum realization, in kg m s⁻¹, of the dimensionless invariant coefficient θ_si. These two quantities have distinct dimensions.^[4]

Let A_U denote the elapsed universe age in the System Frame and n_Tu its corresponding realized temporal count. Then

n_{T u} = \frac{A_{U}}{t_{f}}

The corresponding large-scale radial relation uses the speed of light c, with c = l_f/t_f. Let R_U denote the radius assigned by the universe-scale realization. Then

R_{U} = A_{U} θ_{s i} c

The associated diameter D_U is twice that radius, so

D_{U} = 2 θ_{s i} c A_{U}

These relations tie age and assigned spatial extent together within MQ. They specify a universe-scale geometry under the adopted realization; identifying that scale with a conventional cosmological horizon would require a separate distance mapping.

The Evolution of Mass

The same cosmological allocation relates accumulated mass-equivalent content to elapsed temporal count. Let M_tot be the total realized mass-equivalent content. MQ gives

M_{tot} = n_{T u} m_{f} \frac{{θ_{s i}}^{3}}{2}

Dividing by elapsed age gives the realized global mass-equivalent accretion rate M_acr,

M_{acr} = \frac{{θ_{s i}}^{3}}{2} \frac{m_{f}}{t_{f}}

This is a consequential feature of the MQ cosmological description. At fixed invariant coefficient and fundamental measures, accumulated mass-equivalent content grows in proportion to temporal count. Mass and age therefore share a mathematical dependency in this construction.

Meaning of Mass Accretion

The term "mass accretion" in this context should not be confused with conventional astrophysical accretion, such as matter falling into a star or black hole. Here it describes the MQ relation between accumulated temporal realization and the total mass associated with the universe's count structure.

Thus, as n_Tu increases, M_tot increases in direct proportion. Cosmic evolution is simultaneously temporal, geometric, and material.

The Quantum and Expansionary Epochs

The earliest evolution is treated more fully on the Quantum Epoch page. MQ distinguishes a pre-referenceable configuration description from realized elapsed time. The mapping between those descriptions introduces an explicit normalization in addition to the closure condition.

Let A_qe denote the quantum-epoch configuration extent expressed in a mapped SI-equivalent temporal representation, and A_ee the associated realized expansionary duration. The conversion is

A_{e e} = A_{q e} {(2 θ_{s i})}^{\frac{1}{3}}

With the adopted one-second reference normalization, the reported transition duration is 678,894.26 years. It is not automatically the recombination age or another similarly named epoch in conventional cosmology. The numerical value depends on the mapped normalization as well as the invariant coefficient.^[4]

The earlier logarithmic relation must also retain its reference value. Let R_qe be the integrated configuration radius in the mapped representation, A_qe,0 a positive reference extent, and R_qe(A_qe,0) its reference radius. At fixed fundamental length and coefficient,

R_{q e} (A_{q e}) - R_{q e} (A_{q e, 0}) = \frac{2 l_{f}}{{θ_{s i}}^{3}} \ln (\frac{A_{q e}}{A_{q e, 0}})

The logarithm acts on a dimensionless ratio. The commonly quoted exponential scale additionally chooses zero for the reference radius and one second for the reference extent. That is a normalization of the mapped description, not a physical zero-radius initial state or a clock operating before referenceability. This integrated configuration relation must be distinguished from the realized universe-scale radius above.^[4]

A Universe Divided by Referenceability

MQ assigns fixed geometric referenceability fractions once the invariant coefficient has been selected. Let Ω_obs denote the observable fraction, Ω_dk its complementary dark fraction, Ω_vis the visible fraction, and Ω_uobs the unobserved part of the observable domain. These are upright domain constants, not independently fitted present-day density parameters. Their numerical values inherit the coefficient calibration.

Ω_{obs} = \frac{4}{{θ_{s i}}^{2} + 2}

Ω_{dk} = \frac{{θ_{s i}}^{2} - 2}{{θ_{s i}}^{2} + 2}

Ω_{vis} = \frac{2}{θ_{s i} ({θ_{s i}}^{2} + 2)}

The complementary identities are Ω_obs + Ω_dk = 1 and Ω_uobs = Ω_obs − Ω_vis. For the adopted calibration, the respective fractions are about 31.6376%, 68.3624%, 4.84883%, and 26.7887%. “Unobserved” here belongs to the observable domain. The dark fraction is a geometric referenceability allocation; equating it to a measured dark-energy density requires additional cosmological assumptions.^[4]

Related interpretations are developed in MQ’s discussions of the CMB power spectrum and the universe without curvature.

The Cosmic Microwave Background as an Evolutionary Constraint

The cosmic microwave background provides an important bridge between the early count evolution and the present state of the universe. MQ relates the mass-energy allocation associated with the expansionary transition to a radiation energy density and then to a CMB temperature.

Let M_CMB be the adopted CMB mass-equivalent allocation, V_U the spherical realized universe volume, ρ_CMB the radiation energy density in J m⁻³, a the radiation constant in J m⁻³ K⁻⁴, and T_CMB the CMB monopole temperature in K. The circle constant π is upright. The calculation uses

ρ_{CMB} = \frac{M_{CMB} c^{2}}{V_{U}}

T_{CMB} = {(\frac{ρ_{CMB}}{a})}^{\frac{1}{4}}

Earlier evaluations reported about 2.7251 K. The updated calculation uses the measured temperature to reconstruct age and then recovers 2.72548(57) K through the same relations. D. J. Fixsen’s The Temperature of the Cosmic Microwave Background reports the input value, 2.72548 ± 0.00057 K. The recovered temperature is a shared-input consistency check, rather than an independent prediction of both cosmic age and temperature.^[3]^[4]

The relation can be reversed to infer age from the measured CMB temperature. The adopted geometry gives V_U = (4π/3)(A_Uθ_sic)³, while the allocation is M_CMB = M_acrA_ee. Combining these with the radiation relation and the fundamental relation gives

A_{U} = {(\frac{3 p_{s i} A_{e e}}{4 π a c l_{f} {T_{CMB}}^{4}})}^{\frac{1}{3}}

The adopted reconstruction gives 13.7943(38) billion years. The parenthetical digits express an input-propagated standard uncertainty of 0.0038 billion years; they exclude unquantified uncertainty in the geometry, mass-equivalent allocation, and absolute mapped normalization. The temperature selects the epoch within the construction. Substituting this inferred age back into the same temperature relation checks algebraic closure and does not supply an independent CMB test.^[2]^[4]

Expansion and the Two Frames

MQ assigns two physical comparison frequencies to the frame realizations of the same count construction. Their dependence on age is explicit; identifying either one with a cosmological metric expansion rate requires the corresponding mapping and dynamics.

For this comparison, the expansion-specific metric differential is the dimensionless coefficient offset Δ_H = θ_si − π. Here Δ_H names the offset and both Δ and π are upright.

Let H_sys and H_int denote the System Frame and Internal Frame-resolved comparison frequencies, respectively. Both are physically realized rates. With age expressed in seconds, the formulas yield s⁻¹.

The System Frame expression is

H_{sys} = \frac{π}{θ_{s i} A_{U}}

while the Internal Frame expression is

H_{int} = \frac{2 θ_{s i} - π}{θ_{s i} A_{U}}

For the adopted age and calibration, the reported values are 68.259(19) and 73.508(20) km s⁻¹ Mpc⁻¹, respectively. Conversion from s⁻¹ multiplies the numerical frequency by the number of kilometers in one megaparsec. These two values share their inputs; they are not two independent calibrations. Their comparison with observations is discussed in the Institute’s Hubble-tension paper. The fixed-diameter rates here must not be conflated with that paper’s separately defined age-offset comparison rates.^[5]

The corresponding cosmological terms are conditional conversions of these frequencies. Let Λ_sys be the term formed from H_sys, and Λ(H_int) the same conversion evaluated at H_int. MQ identifies the dark fraction with the density fraction used in this conversion. Then

Λ_{sys} = \frac{3 Ω_{dk} {H_{sys}}^{2}}{c^{2}}

Λ (H_{int}) = \frac{3 Ω_{dk} {H_{int}}^{2}}{c^{2}}

These terms have units m⁻². Because the comparison frequencies depend on age, the expressions do not by themselves establish a time-independent cosmological constant or a complete cosmological expansion history. In particular, the assigned diameter is proportional to age, whereas the comparison frequency includes a coefficient factor. Their identification as one metric expansion law needs an additional mapping argument.^[5]

Evolution as a Unified Count Process

Taken together, these relations produce a markedly different conception of cosmic evolution.

The universe begins, in the MQ description, when discrete structure meets the stated conditions for referenceability. The minimum closure geometry gives a finite realized scale. After realization, temporal count accumulates in the time reference, and the same cosmological allocation links mass-equivalent content and spatial extent to elapsed age. The quantum-to-expansionary conversion retains its mapped normalization. A radiation allocation and the measured CMB temperature then reconstruct the present age used in the two comparison frequencies.

A Unified Count Process

The relations form a connected proposed account of origin, duration, mass-equivalent content, spatial extent, radiation temperature, geometric partition, and expansion comparisons. Their shared structure explains why agreement in one quantity cannot automatically be counted again as independent evidence for another.

The conceptual consequence of the MQ treatment is that physical measures are realized from an evolving count structure rather than supplied as an independently existing continuum. This is the framework’s proposed architecture; the physical adequacy of each cosmological realization depends on its own assumptions and tests.

The distinction also clarifies what "evolution" means in MQ. It is not simply change in the positions of matter as a function of an external time coordinate. Evolution is the progressive realization of physical relations as the temporal count advances. At every stage, what can be physically referenced is constrained by the discrete structure from which observable geometry is produced.

Within this account, the fundamental measures appear in the expressions relating cosmic age, size, mass-equivalent content, thermal state, geometric partitions, and comparison frequencies. Accumulated count connects the minimum referenceable configuration to the proposed present state; that mathematical connection does not by itself establish a uniquely measured cosmic history.

The broader implication is that cosmological history becomes a problem in the evolution of measure itself. MQ proposes that once the rules governing physical referenceability are specified, the history of the universe can be followed from the first realizable geometry to the present cosmological state without abandoning the discrete measurement structure that defines its beginning.

For the formal origin treatment, see Measurement Quantization: A First-Principles Origin of the Universe. Related MQ treatments include Diameter & Age of the Universe as a Function of the CMB Temperature and the Institute's current discussions of mass accretion, fundamental measure, and cosmological geometry.

[1] Jody A. Geiger, Measurement Quantization: A First Principles Origin of the Universe. Public preprint, February 2026. Appendices C.7–C.8 describe minimal closure and the initiation theorem; D.2 and G.2 distinguish contractible-cycle closure from defect-associated holonomy. These are conditional mathematical claims of the proposed framework.

[2] Jody A. Geiger, Diameter & Age of the Universe as a Function of the CMB Temperature. Public preprint, first listed February 2021. It supplies historical context for the temperature-to-age construction; its older frame terminology and dimensional conventions are not adopted here.

[3] D. J. Fixsen (2009), The Temperature of the Cosmic Microwave Background, The Astrophysical Journal 707, 916–920. Accessible author manuscript. Its reported 2.72548 ± 0.00057 K is a temperature measurement, not a direct cosmic age measurement.

[4] Current realization scope. Jody A. Geiger, author-supplied revisions of Diameter & Age of the Universe as a Function of the CMB Temperature, Quantum Epoch, and Increasing Universal Mass, dated October 15, 2026, with foundational clarification recorded November 2, 2026. These revised versions were available to the editor but are not established here as publicly accessible. The public preprints above provide historical context. The page displays the relations linking spherical geometry, mass-equivalent allocation, blackbody radiation, and age. The one-second reference fixes an absolute mapped normalization rather than deriving it from geometric closure. Additional radiation-production history and uncertainty in these physical premises are not independently determined by this calculation. The four normalization/selection inputs are distinct from the CMB epoch selector; electron mass and Bohr radius have shared constant dependencies.

[5] Expansion interpretation. Jody A. Geiger (2025), Resolving the Hubble tension 68.261 and 73.510 km s−1 Mpc−1 AIP Advances 15, 075134. The present frequency and cosmological-term formulas follow the author’s later October 23, 2026 manuscript treatment, available to the editor but not established here as publicly accessible. They are physically realized comparison frequencies with shared age dependence. The displayed diameter and those frequencies do not alone determine the metric expansion, source dynamics, or radiation history. Numerical agreement is not assigned independent statistical significance here.

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