Appendix 6
Appendix 6. Classical Periodization of the Universe’s Evolution
Note 22
this is not the Hubble radius, RH=c/H(z), and not the “particle horizon at that time”.
Today (event) / Today / Now
The present moment is the peak of the Λ-domination epoch. The Universe has reached an age of almost 14 billion years, and accelerated expansion is fully determined by “dark energy”.
| start | end (now) | |
| z | 0 (by definition) | |
| t, s | 4.35495×10¹⁷ | |
| t, yr | 1.37970×10¹⁰ | |
| R, m | 4.36520×10²⁶ |
- Cosmological parameters (Planck 2018):
- ΩΛ = 0.6847 (dominant contribution)
- Ωm = 0.3153 (secondary contribution)
- Ωr = 9.1×10-5 (negligible)
Radius-change drivers: accelerated expansion driven by the Λ term; matter and radiation no longer play the leading role.
Λ-domination / Λdom
The Λ-domination epoch began when the “dark energy” density became equal to the matter density. From that point onward, the cosmos transitioned to accelerated expansion, and the Λ term has governed the Universe’s dynamics up to the present time.
| start | end (now) | |
| z | 0.29497 (equality moment ρm a-3 = ρ_Λ) | 0 (by definition) |
| t, s | 3.12105×10¹⁷ | 4.35495×10¹⁷ |
| t, yr | 9.88900×10⁹ | 1.37970×10¹⁰ |
| R, m | 3.00890×10²⁶ | 4.36520×10²⁶ |
Radius-change drivers: dominance of the Λ term and accelerated expansion. Matter remains secondary, and the radiation contribution is negligible. The possible range of radius estimates at the beginning of the epoch depends on how the equality boundary is defined (using the mean Planck 2018 parameters or accounting for the Ωm and ΩΛ uncertainties); the spread does not exceed 1–2%.
Large-scale structure formation / Struct Form
Post-reionization growth of gravitational instabilities: dark matter halos, galaxies, groups, and clusters form; the “cosmic web” emerges. Matter dominates; the Λ contribution grows and reaches equality with matter at the epoch boundary.
| start | end | |
| z | 5.6768 | 0.29497 |
| t, s | 3.15576×10¹⁶ | 3.12105×10¹⁷ |
| t, yr | 1.00000×10⁹ | 9.89001×109 |
| R, m | 6.53780×10²⁵ | 3.0089×10²⁶ |
Radius-change drivers: matter domination (growth of density contrasts) and a gradual strengthening of Λ toward the epoch boundary. The possible range for Rstart (on the order of a few percent) is due to the fact that z(t) at ~1 Gyr is obtained by inverting the FRW relation in the matter-dominated regime; refining the parameters (H0, Ωm) and accounting for a small radiation correction produce minor shifts. The endpoint (zend, Rend) is fixed strictly by the equality ρm a-3 = ρ_Λ.
Reionization / Re‑ion
Transitional period in which the first ionizing background from stars/quasars gradually “opens windows” in the intergalactic medium, driving hydrogen into the ionized state. Structures are already forming, but the large-scale pattern of the “cosmic web” is only beginning to strengthen.
| start | end | |
| z | 9.5913 | 5.6768 |
| t, s | 1.57788×1016 | 3.15576×1016 |
| t, yr | 5.00000×108 | 1.00000×109 |
| R, m | 4.12151×1025 | 6.53780×1025 |
Radius-change drivers: matter domination; the growth of the first ionization sources increases the medium’s transparency, but the Λ term still has almost no effect on the expansion dynamics. The possible range for Rstart is related to refining z(t): in full ΛCDM, with a small radiation correction included, the value decreases by approximately 0.1–0.3% (i.e., R1 ∼ 4.11–4.12×10²⁵ m).
Cosmic Dawn / Cosm Dawn
Period of the first light sources (the first stars and protogalaxies); the preconditions for an ionizing background are established, which will later lead to reionization.
| start | end | |
| z | 20 | 9.5913 |
| t, s | 6.31152×10¹⁵ | 1.57788×10¹⁶ |
| t, yr | 2.00000×10⁸ | 5.00000×10⁸ |
| R, m | 2,07867×10²⁵ | 4.12151×10²⁵ |
Radius-change drivers: matter domination; the Λ contribution is negligible. The possible range for radiuses within ≈ ±(0.1–0.3)% is related to whether a small radiation correction is included and to the exact choice of Planck 2018 parameters.
Dark Ages / Dark Ages
Interval after recombination, when the Universe was transparent but no light sources yet existed. The gas consisted mainly of neutral hydrogen and helium. During this time, the first gravitational fluctuations formed, but stars and galaxies had not yet ignited.
| start | end | |
| z | 1020 | 20 |
| t, s | 1.34100×10¹³ | 6.31152×10¹⁵ |
| t, yr | 4.25000×10⁵ | 2.00000×10⁸ |
| R, m | 4,27542×1023 | 2,07867×10²⁵ |
Radius-change drivers: matter domination, with a partial radiation contribution in the early phase; expansion slows compared with the radiation-dominated epoch, but the Λ term is still negligible. The radius range depends on where the end of the “Dark Ages” is placed (the emergence of the first light sources: z ≈ 30–15); this choice can shift R by ~±10%.
Recombination / Light
Epoch when protons and electrons combined into neutral hydrogen and helium. The Universe became transparent to radiation—this is when the Cosmic Microwave Background (CMB) originated, which we observe today. A short interval (about 10⁵ years) after the Big Bang, when the temperature dropped to ≈ 3000 K and electrons recombined with protons, making the Universe transparent to radiation. Redshift z ≈ 1100. Recombination is a narrow transitional stage between the plasma phase and the transparent phase.
| start | end | |
| z | 1180 | 1020 |
| t, s | 1,04440×1013 | 1.34100×10¹³ |
| t, yr | 3.31000×10⁵ | 4.25000×10⁵ |
| R, m | 3,69619×1023 | 4,27542×1023 |
Radius-change drivers: matter domination with a noticeable radiation contribution; the expansion rate gradually decreases. The possible radius range is determined by refining the criterion for the “end of recombination” (accounting for z ≈ 1089.92 from Planck 2018), which can change R by approximately 15–16%.
Matter domination / Matter
After radiation–matter equality, the expansion dynamics becomes governed by matter (primarily “dark” matter). The plasma is still opaque, but the scale factor already grows according to the matter-law. The epoch ends at the onset of recombination.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1,48321×10¹² (radiation–matter equality) | 1,04440 ×1013 (onset of recombination = 331 000 yr) |
| t, yr | ||
| R, m | 1,27418×10²3 | 3,69619×10²3 |
Radius-change drivers: matter-dominated ΛCDM dynamics, with R∝a∝t2/3.
Photon domination / Photon
After nucleosynthesis, the Universe remains in a state of hot ionized plasma. Photons are tightly coupled to baryons (via electrons), and they govern the dynamics: the plasma is opaque, and photons cannot propagate freely. Radiation-dominated evolution continues up to Recombination.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.20000×10³ | 1.48321×1012 |
| R, m | 7,4480×10¹² | 1,27418×10²3 |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R∝t1/2.
Big Bang nucleosynthesis / BBN
Period when, at temperatures on the order of 10⁹ K, during the first minutes of the Universe, light nuclei began to form—deuterium, helium-3, helium-4, and lithium-7. The balance of processes set the present-day H/He ratio. The radius evolution follows radiation-dominated dynamics.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.80000×10² | 1.20000×10³ |
| R, m | 2.8580×10¹² | 7.4480×10¹² |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R∝t1/2.
Neutrino epoch / Neutrino
During this period, neutrinos cease to interact effectively with matter and “decouple” from the plasma. They begin to propagate freely through the Universe, forming the relic neutrino background. Radiation-dominated dynamics continues.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10¹ | 1.80000×10² |
| R, m | 6.7400×10¹¹ | 2.8580×10¹² |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R ∝ t¹⁄²; increasing time from 10 to 180 s (×18) increases the radius by a factor of 4.2426.
Lepton epoch / Lepton
Phase when the Universe’s dynamics is governed by leptons (electrons, muons, neutrinos, and their antiparticles). At temperatures ~10¹⁰ K, active lepton annihilation and interaction processes occur. By the end of the epoch (a few seconds after the Big Bang), most leptons annihilate; an excess of electrons remains, which is required for subsequent atom formation.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁰ | 1.00000×10¹ |
| R, m | 2.13220×10¹¹ | 6.7400×10¹¹ |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R ∝ t1/2; increasing time from 1 to 10 s (×10) increases the radius by a factor of ≈ 3.1623.
Hadron epoch / Hadron
Period when the Universe’s temperature dropped enough for quarks to cease existing as a plasma and bind into stable hadrons—protons and neutrons. By the end of the epoch, hadrons annihilate with antihadrons; a small baryon excess remains, which determines present-day matter. The radius evolution corresponds to the radiation-dominated phase.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻⁶ | 1.00000×10⁰ |
| R, m | 2.13220×108 | 2.13220×10¹¹ |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R ∝ t¹⁄²; increasing time from 10⁻⁶ to 100 s (×10⁶) increases the radius by a factor of 1000.
Quark–gluon plasma / QGP
Stage when the Universe was so hot (T ≈ 10¹² K) that quarks and gluons did not form bound states (hadrons) but existed as a dense plasma. As the temperature dropped below the characteristic scale, quarks began to bind into nucleons. Radii are computed using the ΛCDM scaling R ∝ t¹⁄².
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻¹² | 1.00000×10⁻⁶ |
| R, m | 2.13220×10⁵ | 2.13220×108 |
Radius-change drivers: radiation-dominated ΛCDM dynamics, with R ∝ t¹⁄²; over the interval from 10⁻¹² to 10⁻⁶ s (an increase by 10⁶), the radius grows by √10⁶ = 1000.
Electroweak symmetry breaking (event) / ElWeak
Transition in which the W± and Z₀ fields acquire mass, and the electromagnetic interaction separates from the weak interaction.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻¹² | 1.00000×10⁻¹² |
| R, m | 2.13220×10⁵ | 2.13220×10⁵ |
Radius-change drivers: none.
Radiation‑dominated plasma / RAD
Hot ultra-relativistic plasma (leptons, photons, neutrinos, and at the earliest times—quarks/gluons). The scale dynamics is radiation-like: a ∝ t¹⁄². At the end of the epoch, electroweak separation occurs (event).
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻²⁸ | 1.00000×10⁻¹² |
| R, m | 2.13220×10⁻³ | 2.13220×10 |
Radius-change drivers: from 10⁻²⁸ to 10⁻¹² s, the Universe evolves in a “radiation-like” regime, where the characteristic scale grows as the square root of t.
Reheating / REH
Very short phase after inflation, when the inflaton energy is transferred into a hot particle plasma. Radii are taken from standard cosmology: once the plasma is established, the scale factor grows as in radiation domination, a ∝ t¹⁄²
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻³² | 1.00000×10⁻²⁸ |
| R, m | 2.1322×10⁻5 | 2.13220×10⁻³ |
Inflation / INFL
Short phase of exponential expansion of the Universe. Here the radius grows as R ∝ eHt; the growth is specified via the number of e-folds. For the baseline, we take N = 60 e-folds (typical range 50–60), which addresses the classical horizon and flatness problems.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻³⁶ | 1.00000×10⁻³² |
| R, m | 1.86710×10⁻³¹ | 2.1322×10⁻5 (growth by e60 ≈ 1.1420×10²) |
Radius-change drivers: exponential growth R → R·eN with the chosen N = 60 provides the required “smoothing” of the metric prior to reheating.
Grand Unification / GUT
Interval prior to inflation in which (in the model picture) the strong and electroweak interactions are indistinguishable; X/Y boson decays and the emergence of baryon asymmetry are allowed.
| start | end | |
| z | not relevant prior to Recombination | |
| t, s | 1.00000×10⁻⁴³ | 1.00000×10⁻³⁶ |
| R, m | 5.90418×10⁻³⁵ | 1.86710×10⁻³¹ |
Radius-change drivers: radiation-dominated ΛCDM evolution; the radius growth is consistent with the scale factor, and radii are matched at the boundary with inflation.
Planck epoch / PLANCK
The Planck epoch opens the history of the Universe—an interval in which the laws of quantum gravity governed the dynamics of space and matter. The ΛCDM model is formally not applicable here, because for t < tₚ (5.39×10⁻⁴⁴ s) the theory breaks down. In the QoQ model, space began from a single fundamental hypercube of dimension 100, and within this epoch only one SER expansion step occurred, producing an ensemble of 200 Space Quanta of dimension 99. Thus, the Planck epoch is the moment of the Sacrifice of the Primordial, when the first step in the unfolding of the Universe was made.
| START | end | |
| z | formally → ∞ (temperature and density are infinite) | |
| t, s | 5.39130×10⁻⁴⁴ | 1.00000×10⁻⁴³ |
| t, yr | 1.71000×10⁻⁵¹ | 3.17000×10⁻⁵¹ |
| R, m | 1.61626×10⁻³⁵ (Planck length) | 5.90418×10⁻³⁵ (by the SER rule, growth from 1 to 200 SQ) |
Radius-change drivers: quantum-gravitational dynamics and the first SER step (100→99). Within ΛCDM, the radius is not defined at this point, but in the model it is set by the discrete expansion of fundamental hypercubes.
Appendix 6. Classical Periodization of the Universe’s Evolution
Appendix 6