Cosmology

Cosmology is the study of the universe as a whole: how it expands, what it contains and how the expansion will end. The expansion is tracked by the scale factor, the number that multiplies the distances between distant galaxies. In the Broken-Born program, the scale factor of our universe and that of its momentum-space description, the conjugate universe, are exact reciprocals, so one grows as the other shrinks, in the way a waveform’s spectrum narrows when the waveform is stretched. Dark energy, which accelerates the expansion, is identified with a field: the angle τ that sets how the vacuum divides phase space, the space of positions and momenta taken together, into position and momentum. The field’s energy density may fall as space expands but never rise. That requirement is the one the most recent survey data lean against, so dark energy is where the program faces its nearest observational test. This section sets out the established cosmology the claims use, then the claims in the order the program derived them.

Stands: the cosmological constraint a·ã = 1, the duality dictionary, the turnaround as the conjugate bounce (premise unresolved), τ as hilltop quintessence (under pressure), τ’s fifth-force safety, the no-phantom bound w ≥ −1 (under pressure), the dark-energy over-constraint · Died: conjugate collapse powers our expansion · Open: dual kinetic energy versus τ’s potential, the sign of V(τ) and the turnaround · Superseded: the heuristic rule w_eff = −2 − w̃, the potential’s origin in the rigid ω, the earlier readings of DESI · Conjectures: the phase-space diameter relation (chat-only)

Map#

The section has three subsections. The first two each open with established physics and then give the program’s own claims; the third is established physics only. None of the program’s cosmological claims is machine-checked: they are derived [D] in the lab notebook (#1 §4, §6–§7) and, except for τ’s fifth-force safety (#1 §4 only), restated in the checkpoint (#11 §10), with literature fits [T] for the dark-energy sector.

Scale-factor duality comes first, because the rest of the section is written in its terms. It starts from established physics, Friedmann cosmology and minisuperspace, the standard description of a uniform expanding universe reduced to its scale factor and lapse, and redshift, the stretching of every wavelength by the expansion, and then gives the program’s results in derivation order: the reciprocal relation a·ã = 1, which follows from the rigidity of the symplectic form; the dictionary w_eff = −w̃ that translates energy in the conjugate description into its effect on our expansion, with the superseded heuristic it replaced; the obituary of the founding idea that the conjugate universe’s collapse drives our acceleration, killed once by data and once by the corrected dictionary; and the reading of a far-future turnaround as the conjugate universe’s bounce. It ends with an open gap in the motivation for dark energy and a chat-only conjecture.

Dark energy comes second. Its first eight pages are established physics: the cosmological constant Λ, the dark energy of the standard model, and de Sitter space, the future it leads to; quintessence and the equation of state w, with the thawing and freezing classes and axion-like fields, whose periodic potential τ is given; the CPL parametrization in which surveys report a changing w; the phantom divide at w = −1; and the baryon-acoustic-oscillation survey of the Dark Energy Spectroscopic Instrument (DESI). The program’s claims follow: the dark-energy field τ, its safety from fifth-force tests, the bound w ≥ −1, the record of the DESI release that favours a crossing below −1, the over-constraint that ties the model’s parameters together, and the open conflict over the sign of τ’s potential. The documents write the potential as V₀[1 + cos(τ/f)], which is never negative for V₀ > 0, while the turnaround needs it to become negative; no document resolves the conflict (flag 27 in review/wiki-build-flags.md), and both the turnaround page and the over-constraint’s turnaround time rest on it.

Early-universe cosmology is literature only: the thermal history of the radiation era and its count of light species, including those of a hidden sector at its own temperature; the two observations that measure them, Big Bang nucleosynthesis and the cosmic microwave background; the relic yield Y = n/s and entropy dilution and inflation and the dilution of relics; and gravitational waves from phase transitions. It is background for row 10 of the predictions table, whose a⁻⁶ step in the strength of gravity comes from the dual gravity term on the Friedmann page, and for the review that retired the soliton dark-matter candidate.

Boundaries#

• Where τ comes from geometrically, as the phase of the modular field’s boundary value, is τ as the Maslov phase of the boundary; the modular inversion whose |Z| = 1 locus is identified with a·ã = 1 (an identification queried in flag 23 of review/wiki-build-flags.md) is reciprocity as modular inversion.
• Where τ’s potential comes from is open: Open: the origin of the ρ-preserving potential.
• The observational tests are rows of the predictions table: row 4, row 5 and row 10.
• The conjugate universe as a concept, one state with two descriptions, is the conjugate universe.
• The vacuum energy of the spin-2 sector is the vacuum-energy identity, with its scope limit on the cosmological-constant problem; the cosmological solutions of bimetric gravity are bimetric cosmology.
• Monopole relics and how defects form in phase transitions are magnetic monopoles.