Dark energy

Dark energy is the name for whatever makes the expansion of the universe accelerate; in the standard cosmological model it is a cosmological constant, an energy density that stays the same as space expands. The Broken-Born program identifies it instead with a field, τ, the angle that sets how the vacuum divides phase space, the space of positions and momenta taken together, into position and momentum. As a field, τ can change, and the program requires the change to go one way: dark energy may weaken, but its density may never rise as space expands, the behaviour called phantom. The second data release of the Dark Energy Spectroscopic Instrument (DESI) favours a phantom phase at earlier times, so the requirement stands against the direct reading of the data and the sector is under real pressure; the next release is the decisive test. This section holds the established physics of dynamical dark energy, the program’s τ sector, the record of the data that test it, and one unresolved conflict in its documents.

Stands: the established physics of the cosmological constant Λ, de Sitter space, quintessence and the equation of state, thawing and freezing quintessence, axion-like fields and pseudo-Goldstone bosons, the CPL parametrization w(a) = w₀ + wₐ(1 − a), the phantom divide and the null energy condition and DESI baryon acoustic oscillations; the program’s claims τ: hilltop quintessence on the Maslov circle ([D + T], under real pressure), fifth-force safety of τ ([D], lab notebook only), the no-phantom bound w ≥ −1 ([D + T], under real pressure) and the dark-energy over-constraint ([D], a count); and the record of DESI DR2’s phantom crossing, the measurement that puts the sector under pressure · Died: nothing in this section; the related obituary conjugate collapse powers our expansion is in scale-factor duality · Open: the sign of V(τ) and the turnaround, an unresolved conflict between the potential and the turnaround (in open problems) · Superseded: no page of its own here; folded sections on the potential’s origin in the rigid ω and the earlier readings of DESI (both in superseded statements)

Map#

The first eight pages are established physics, written from general knowledge and tagged [T]; the six after them are the program’s claims, the record of the data that test them, and an open conflict. The program’s claims are stated in checkpoint #11 §10, in a paragraph tagged [D + T], and were first set out in §7 of the lab notebook; fifth-force safety is argued in the notebook’s §4 only. No verify/ script tests the cosmology.

The literature comes first.

  • The cosmological constant Λ is the baseline: a constant term in Einstein’s equations that acts as an energy density of empty space, with w = −1 exactly, the dark energy of the standard model ΛCDM. The page shows why it does not thin as space expands, how a positive Λ makes the expansion accelerate toward de Sitter space while a negative one halts and reverses it, how surveys test for a departure from w = −1, and why the vacuum energy of quantum fields acts as a Λ. It is the standard expectation of row 4 and row 5, and the program uses it in four ways: τ in its place, dual kinetic energy acting as a Λ, the constant terms of the bimetric potential, and the negative effective Λ that the turnaround needs.
  • De Sitter space is the spacetime of a universe that contains only a positive Λ: a constant Hubble rate, exponential expansion with Λ = 3H², maximal symmetry and a horizon around every observer, with anti-de Sitter space as the counterpart for a negative Λ. It is the far future that row 5 calls “Eternal de Sitter”, the background on which a massive spin-2 field must satisfy the Higuchi bound, and, in two dimensions, the space of values of the field K in model I.
  • Quintessence and the equation of state introduces dark energy as a scalar field: the equation of state w, why a field with mostly potential energy has w near −1, the field equation with its expansion damping, short summaries of the thawing and freezing classes, of hilltop and axion-like potentials and of the two-parameter form of the CPL page, and recollapse when the vacuum energy turns negative. It ends with the fits of quintessence models to recent data that #11 cites, live-searched [S].
  • Thawing and freezing quintessence gives the two classes in full. A thawing field is held near w = −1 by the expansion and departs from it late; a freezing field moves early and slows toward −1. The page shows why a thawing field’s initial velocity drops out, places hilltop models in the thawing class, and locates each class in the w₀–wₐ plane, with the corridor wₐ ≈ −1.5(1 + w₀), for which no document gives a reference. It sets DESI’s second data release against the class, with flag 43 in review/wiki-build-flags.md on where the corridor lies relative to the release’s crossing, and states the thawing drift of τ that row 4 requires.
  • Axion-like fields and pseudo-Goldstone bosons explains the potential τ is given: a field that is an angle, kept light and coupled only through its derivatives by a shift symmetry, with the periodic potential V₀[1 + cos(φ/f)] left by a small explicit breaking. It covers the axion itself and axion-like fields as dark matter and as dark energy, and the program’s uses: τ’s hilltop potential and fifth-force safety, the toy models’ pseudo-Goldstone polarization angle, the momentum graviton X called “axion-like” for its exact shift symmetry, and the wave-island field χ produced “like an axion”.
  • The CPL parametrization w(a) = w₀ + wₐ(1 − a) gives the two-number Chevallier–Polarski–Linder form in which surveys report a changing w and the program states its requirement: a first-order expansion in the scale factor, the redshift form and its early-time limit, the meaning and sign of w₀ and wₐ, the decorrelated pivot form, and what two numbers cannot represent. It places thawing models in the w₀–wₐ plane, with the program’s corridor wₐ ≈ −1.5(1 + w₀), for which no document gives a reference, and shows how a fit expresses a phantom crossing, w₀ > −1 with w₀ + wₐ < −1, the shape that DESI’s second data release favours. A fit in that region does not by itself show a crossing: the page reports flag 43 in review/wiki-build-flags.md, which places the program’s corridor there too and finds the difference from the release’s crossing in the slope.
  • The phantom divide and the null energy condition explains why w = −1 separates dark energy that weakens from dark energy that strengthens, shows that a canonical scalar obeys the null energy condition because ρ + p is a square, lists what a phantom phase or a crossing would need (a ghost, several fields, non-minimal couplings, dark-sector interactions), and separates an intrinsic phantom from an inferred one, the distinction the program’s kill condition depends on.
  • DESI baryon acoustic oscillations describes the survey whose releases test the program: the sound-horizon ruler and its Fourier form, how the ruler gives distances across and along the line of sight, why w(z) is inferred from those distances by fitting a model rather than observed, and the data releases from Data Release 1 (DR1) to DR3 as the documents cite them.

The program’s claims follow.

  • τ: hilltop quintessence on the Maslov circle is the central claim [D + T]: dark energy is τ, the angle around the Maslov circle of the space of polarizations, with action S_τ and potential V₀[1 + cos(τ/f)], sitting near the maximum and thawing along the corridor wₐ ≈ −1.5(1 + w₀). The page traces τ to the corrected postulate P2′, gives the tags of each part of the potential, records that the wedge sector of the momentum graviton adds no competing vacuum energy, sets out the pressure from DESI’s Data Release 2 (DR2), with flag 43 on where the corridor lies relative to DR2’s crossing, and shows what the toy models establish: τ’s circle is their Goldstone angle, which shows consistency and nothing more. A folded section records the superseded v0.1 account of the potential’s origin.
  • Fifth-force safety of τ checks that so light a field produces no detectable force between ordinary bodies: as a pseudo-Goldstone field it couples only through its derivatives, with no tree-level Yukawa coupling [D]. The page explains the standard protection of axion-like fields, records that the argument exists only in the lab notebook’s first version, and contrasts the momentum graviton X, which is safe by its short range instead.
  • The no-phantom bound w ≥ −1 is the sector’s sharpest commitment: τ is a canonical scalar, so whatever the potential its energy density never grows as space expands, and w never falls below −1 while that density is positive. The page gives the three-step derivation, the distinction between an intrinsic and an inferred phantom phase, the kill condition with the documents’ differing statements of how much it kills (#11: the whole framework), and the pressure from DR2.
  • DESI DR2’s phantom crossing is the record of the measurement: in every dataset combination the favoured w(z) is above −1 at low redshift and crosses below it above z ≃ 0.4. The page sets out the two points on which the sector survives, how the finding entered the program through the round-3 review and #11 v2.1, the italic sentence of #11 §10 that still reads DESI’s hints as “exactly the required drift”, and the three outcomes of Data Release 3 (DR3). A folded section lists the earlier, superseded readings of DESI.
  • The dark-energy over-constraint counts parameters: with V₀ fixed by the measured dark-energy density, two numbers (f, τᵢ) must fit three observables (w₀, wₐ, t_turn), one relation that #11 §15 counts as a progressive sign. Its third observable is long-horizon and rests on the open sign problem.
  • Open: the sign of V(τ) and the turnaround closes the section with an unresolved conflict in the documents: V₀[1 + cos(τ/f)] is never negative for V₀ > 0, yet the turnaround and the fits cited for it need negative vacuum energy. None of the three documents that write the potential discusses it; the wiki’s build recorded it for Paul’s ruling as flag 27 in review/wiki-build-flags.md, with an executed check kept outside the gate. The page lists what depends on it and records the conflict without choosing a side.

Boundaries#