Cosmology
From the cascade to the observable universe
Cosmogony explains how structure opens; cosmology explains how that structure is measured. This page starts from the stabilised cascade and follows what becomes observable: expansion, dark sector, H₀, neutrinos, and tests.
After cosmogony: late geometry, dark budget, Hubble tension
Plain language
What cosmology adds to cosmogony
The Cosmogony page describes a primordial cascade outside ordinary chronology: persistence thresholds organise, 2 becomes a boundary, 3, 5, and 7 form the active core, then the structure stabilises around the reduced attractor μ* = 15.
Cosmology begins after that move. It is not a second Big Bang story; it asks how this structure becomes readable as a measurable universe: proper duration, three directions of space, expansion, matter-energy budget, and observational signatures.
The useful image is a map becoming readable. Cosmogony draws the deep coordinates; cosmology studies how those coordinates appear to an internal observer, that is, in quantities that are actually measured.
In this reading, visible matter is baryonic matter coupled to light: atoms, gas, stars, dust, galaxies. Informational matter is a component that gravitates and structures without first being ordinary luminous matter. Dark energy is the smooth component read as background pressure and cosmic acceleration.
The important pedagogical point is status separation. H₀, the dark budget, neutrinos, and late dark-energy dynamics belong to one PT chain, but they do not all carry the same evidential level.
Cosmogony
It gives the boundary conditions: thresholds, crystallisation of 2, active core 3·5·7, and reduced attractor 15.
Proper time
Measurable time is not assumed at the start; it appears once geometry carries a temporal signature.
Cosmology
It translates structure into late observables: expansion, dark sector, neutrinos, and sky tests.
Standard
From the sieve to cosmological parameters
Once the cascade has stabilised, the active primes 3, 5, and 7 become the three active directions of geometry. PT relativity reads them as a Fisher-Bianchi I metric: naturally anisotropic before being averaged as an isotropic sky.
In this frame, H₀ is not introduced as a primitive scalar. It is read as the average of three directional rates H₃, H₅, and H₇. The isotropic value is the sky average; some local measurements may sample a different effective direction.
The Hubble tension then becomes more intelligible: it can be read as the gap between a global average and local directional readings, rather than as a mere correction added to the standard model.
The dark sector comes from the trace left by inactive primes. They do not reopen new active spatial directions, but produce echoes: a non-luminous gravitational component, then a smooth component read as dark energy.
3·5·7 → Fisher-Bianchi I → mean H₀ → inactive echoes → Ωinfo / ΩΛ
Standard
The cosmological budget as an echo reading
The diagram is not claiming to show a local dark substance. It separates three readings: visible baryonic matter, the informational component that gravitates without direct light, and the smooth component carrying acceleration.
In the monograph, the total dark sector is tied to the inactive fraction of the sieve. The Ωinfo / ΩΛ split then uses the q⁺/q⁻ bifurcation and a Clausius-type thermodynamic reading.
This step is numerically strong, but it must be tagged correctly: it is a derivation/physical bridge in the PT dictionary, not an unconditional arithmetic theorem.
Ω
Ωb
The visible or baryonic share: matter coupled to electromagnetism, therefore traceable by light.
Ωinfo
The non-luminous gravitational share: it weighs in geometry and organises structures.
ΩΛ
The smooth share: read as background pressure and late cosmic acceleration.
Technical
What is derived, what remains open
The monograph classifies cosmology as a deployment layer and a layer of falsifiable predictions. It does not have the same status as the arithmetic sieve theorems: some relations are derived inside the PT dictionary, some are physical bridges, some are numerical validations, and some remain open.
H₀ is presented as a Fisher-Bianchi reading: H₀ = (H₃ + H₅ + H₇)/3 = 67.41 km/s/Mpc. The Hubble tension is reframed by directional anisotropy, with convergence expected as sky coverage becomes more isotropic.
The total dark sector is tied to the inactive fraction F_echo(N) = 1 - 2/(e^γ ln N). The Ωinfo / ΩΛ split comes from the q⁺/q⁻ transition and Clausius enthalpy. Late dynamics w(z), however, remains a more open frontier.
boundary condition
Cosmogony supplies 2 as boundary, 3·5·7 as active core, and μ* = 15 as reduced attractor.
geometry
The Fisher-Bianchi metric assigns scale factors aₚ = γₚ/μ to the active primes.
Hubble
The isotropic constant is the mean H₀ = (H₃ + H₅ + H₇)/3.
anisotropy
A directional measurement reads H(n) = Σ Hₚ nₚ², reframing the Hubble tension.
inactive primes
Primes below the active threshold leave an echo fraction F_echo(N).
dark sector
Ωinfo and ΩΛ come from q⁺/q⁻ and then the Clausius thermodynamic reading.
neutrinos
Neutrino mass connects the cosmological sector with particle predictions.
frontier
w(z), DESI/Euclid/CMB-S4, and late dynamics remain exposed to data.
DER/VAL
H₀ and several cosmological quantities are derived and then confronted with data.
DER/BRIDGE
The dark-sector split uses a physical bridge: q⁺/q⁻ plus Clausius.
PRED/OPEN
Late dark-energy dynamics should remain presented as a testable programme.
Status
Epistemic status
This page extends cosmogony. The strongest status belongs to the Fisher-Bianchi chain and numerical outputs; interpretations of the dark sector and w(z) must remain separated by evidential level.