Row 4: thawing dark energy, never phantom

Row 4 is the program’s prediction for how dark energy, the cause of the accelerating cosmic expansion, changes over time. The program identifies dark energy with τ, the angle that locates the vacuum’s choice of polarization on a circle; τ has a periodic potential and starts near its maximum, a setup called hilltop quintessence. Such a field makes dark energy weaken slowly ("thaw") and keeps its equation of state w at or above −1, the value of a cosmological constant, so it can never enter the “phantom” regime w < −1. The test is the Dark Energy Spectroscopic Instrument (DESI). Its Data Release 3 (DR3), expected in late 2026, is the decisive one. Its Data Release 2 (DR2) already favours a phantom phase in the past, so the sector is under real pressure. Row 4 is one of the three rows the checkpoint names as the program’s near-term falsification exposure.

Status: Alive, under real pressure — [D + T] (#11 §10), with w ≥ −1 [D] and the thawing shape [T] in the lab notebook (#1 §7) — DESI DR2’s phantom crossing stands against the strict w ≥ −1 (#11 §10, accepted as round-3 ruling 11; root CLAUDE.md: “under real pressure ahead of DR3”); not machine-checked.

The row#

Checkpoint #11 §13, row 4:

“DR3+” means DR3 or a later release. #11 §15 lists the row, with rows 1 and 7, as near-term falsification exposure, and calls DESI’s next release the program’s “nearest trial”.

The observable#

The equation of state w of a component of the universe is the ratio of its pressure to its energy density, p = wρ. Through the continuity equation ρ̇ = −3H(ρ + p), with H the expansion rate, it fixes how the component’s density changes as space expands [T] (quintessence and the equation of state). w(z) is that ratio for dark energy as a function of redshift z, which labels cosmic time by how much the universe has expanded since.

A drifting w is usually summarized by two numbers in the Chevallier–Polarski–Linder (CPL) form w(a) = w₀ + wₐ(1 − a), with a the scale factor, equal to 1 today [T]. w₀ is the present value, and a negative wₐ means that w has been rising toward the present (the CPL parametrization).

No survey observes w directly. DESI measures distances with the baryon-acoustic-oscillation ruler, the imprint of sound waves in the early plasma on the clustering of galaxies, and w(z) follows only after a form for it is chosen and fitted together with other data (from distances to w(z)). That step matters for the kill condition below.

The standard expectation#

“w ≡ −1”: a cosmological constant, an energy density of empty space that does not change as the universe expands. It is the dark energy of the standard cosmological model, ΛCDM, a cosmological constant plus cold dark matter [T] (the cosmological constant Λ).

The Broken-Born requirement#

The field#

#11 §10, tagged [D + T]:

“τ is hilltop quintessence on the Maslov circle, V = V₀[1 + cos(τ/f)], periodicity by topology; strictly w ≥ −1; thawing corridor wₐ ≈ −1.5(1 + w₀); two parameters (f, τᵢ) for three observables (w₀, wₐ, t_turn) — one over-constraint.”

τ is the angle that locates the vacuum’s polarization on the Maslov circle, a circle in the space of ways to split phase space into position and momentum halves (τ as the Maslov phase of the boundary). Because τ lives on a circle, its potential is periodic; the cosine form, with amplitude V₀ and angular scale f, is the standard potential of an axion-like field [T]. τᵢ is the field’s initial value. The field and its action are on τ: hilltop quintessence on the Maslov circle. The requirement has three parts, each with its own derivation.

Thawing#

A field that starts near the top of its potential is held almost still while the expansion rate is high, so its w is close to −1 in the past. As the expansion slows, the field moves off the hilltop, its kinetic energy grows, and w rises [T]. The lab notebook applies this to τ (#1 §7 item 2, transcribed from its LaTeX):

“Thawing shape. Hilltop initial conditions give w ≈ −1 in the past, rising now: w₀ > −1, wₐ < 0, on the standard thawing corridor wₐ ≈ −1.5(1 + w₀).” [T]

The tag is [T]: thawing is a property of hilltop fields in general, not a result of the program (how τ behaves). The corridor is a line in the (w₀, wₐ) plane near which thawing models lie (thawing models in the w₀–wₐ plane); neither #1 nor #11 cites a source for it. Flag 43 in review/wiki-build-flags.md records that every point of the corridor has w₀ > −1 and w₀ + wₐ < −1, the region in which a CPL line passes below −1 in the past and in which DR2’s fits lie, and that no document says so (below).

Never phantom#

The lab notebook’s argument, tagged [D] (#1 §7 item 1, transcribed from its LaTeX):

“w ≥ −1 always. τ is a canonical scalar; the null energy condition holds; phantom crossing is impossible. [D] Any robust measurement of w < −1 (as an intrinsic equation of state, not an artifact of an assumed ΛCDM background) falsifies this sector outright.”

The steps are short. τ has a kinetic term of the standard sign, so for a uniform field the energy density is ρ = ½τ̇² + V and the pressure p = ½τ̇² − V. Then ρ + p = τ̇² ≥ 0, which is the null energy condition, and with ρ > 0 it gives w ≥ −1 [T]. The potential cancels from ρ + p, so no choice of V breaks the null energy condition; the step from it to w ≥ −1 uses ρ > 0, which holds for the positive dark-energy density observed today [T]. Below −1, dark energy would grow as space expands, which τ cannot do (the no-phantom bound w ≥ −1; the phantom divide and the null energy condition). The bound applies to τ as the whole of dark energy, a premise #11 supports with its vacuum-energy identity: “§7.3 guarantees the wedge sector contributes nothing that competes with τ” (#11 §10). Flag 6 in review/wiki-build-flags.md notes that the identity holds for a flat aligned vacuum, which is itself one condition on the gravity sector’s coefficients, so it is not a consequence of symmetry alone.

The drift persists#

“Drift persists in DESI DR3” asks that the next release keep seeing w above −1 and rising, rather than settling on a constant. The sector’s two remaining parameters connect the row to the next one. With V₀ fixed by the measured dark-energy density, w₀ and wₐ fix f and τᵢ, and the turnaround time t_turn of row 5 is then determined: “one over-constraint” (the dark-energy over-constraint). No document computes that relation, and whether t_turn exists at all for the potential as written is unresolved (review/wiki-build-flags.md item 27; the over-constraint’s reach).

What kills it#

Two kill conditions#

• “DR3+ constant −1 (kills τ-sector)”. If DR3 or a later release converges on a constant w = −1, the thawing drift the row requires is absent, and the τ sector dies. v0.1 wrote “DR3+ converging on constant −1” (#1 §9).
• “Robust intrinsic w < −1 (kills outright)”. A phantom equation of state, established as a property of dark energy itself, contradicts the no-phantom bound. “Intrinsic” excludes a w below −1 that appears only because the background model assumed in the fit is wrong: #1 §7 item 1 counts only w < −1 “as an intrinsic equation of state, not an artifact of an assumed ΛCDM background”.

The documents differ on how much the second condition kills. #1 §7 item 1 says “falsifies this sector outright”; #11’s row sets “kills outright” against “kills τ-sector”; and the handoff spells it out as the whole framework. No document states why the scope is wider than the sector (how much a violation kills).

Three outcomes#

The handoff states the test as three outcomes of the next release (HANDOFF.md §2, “External clock”):

DE is dark energy. The third outcome is not specific to the program: other models of dynamical dark energy survive it too. The handoff dates DR3 as “three-year data, expected late 2026”; review/wiki-build-flags.md item 26 records that DR2 already covers three years of operations, and this page quotes the handoff as written. The journey article #10 calls the outcomes “Three doors”: “Constant kills the theory’s heart. Phantom kills it outright. Continued weakening keeps it alive” (‘The referee is already on the field’; the popular articles).

The data situation: under real pressure#

DESI’s second data release reports, in #11’s quotation (§10, from [21S]), that in every dataset combination

“the favored w(z) shows a phase of w > −1 at low redshifts and a phantom crossing to w < −1 above redshifts z ≃ 0.4”

and that this preference “is thus rather independent of parametrization choices made in the analysis”. [21S] is DESI Collaboration (M. Abdul-Karim et al.), “DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints,” arXiv:2503.14738 (2025).

The favoured curve contains both behaviours the row distinguishes. Its low-redshift phase, w above −1 and weakening dark energy, is what the row requires. Its phase above z ≃ 0.4, w below −1, is what the row excludes. #11 §10, in the paragraph “Under pressure (v2.1)”:

“The framework’s strict w ≥ −1 therefore stands against the direct reading of the data. It survives on two points: non-phantom quintessence fits remain compatible [19S], and w(z) is inferred from distances rather than observed, as [21S] also notes. DR3 is the decisive test (§13, row 4).”

The first point rests on fits without a phantom phase, “non-phantom compatible at ~2σ” (#11 §10), citing Gialamas et al., “Quintessence and phantoms in light of DESI 2025,” arXiv:2506.21542 [19S]. The second is the distinction the kill condition already draws between a fitted and an intrinsic w < −1. In this wiki’s reading, both points concern whether the data meet the kill condition; neither is evidence for the bound.

The finding reached the program through the round-3 review, which accepted it as ruling 11 (round-3 rulings), and #11 v2.1 (2026-10-19) added the “Under pressure” paragraph to §10 and the DR2 clause to this row. #11 §15 lists “DESI DR2’s phantom crossing against §10’s strict w ≥ −1” among the program’s degeneration risks. The root CLAUDE.md, which ranks first among the sources, states the position: “DESI DR2 favors a phantom crossing above z ≈ 0.4, against the framework’s strict w ≥ −1 (§10). The dark-energy sector is under real pressure ahead of DR3.”

Flag 43 in review/wiki-build-flags.md bears, in the flags file’s words, “on how row 4’s pressure is stated, not on whether it exists”. In CPL terms DR2’s fits have w₀ > −1 and w₀ + wₐ < −1, and so does every point of the corridor quoted above; in the flag’s audit, fields with τ’s potential that never fall below −1 also gave fits in that region under every fitting convention tried. In the flag’s account, what separates the corridor from DR2’s fits is the slope, which sets where the line crosses −1: at z = 2 for every point of the corridor, at z ≈ 0.35–0.50 for DR2’s fits. The flag concludes that the pressure stands: “It rests on the crossing redshift (DR2 calls the preference ‘rather independent of parametrization choices’), not on the quadrant”, the region of the plane both share. Its audit confirmed it by two independent checks (the corridor and DR2’s crossing).

The full record, including an italic passage of #11 §10 that still reads DESI’s hints as “exactly the required drift” and is unreconciled with the paragraph above, is on DESI DR2’s phantom crossing.

What the row does not depend on#

• The sign of the potential. The far-future turnaround of row 5 needs V(τ) to become negative, which the potential as written never does for V₀ > 0 (review/wiki-build-flags.md item 27; Open: the sign of V(τ) and the turnaround). In this wiki’s reading that conflict does not touch row 4: thawing concerns the field near the potential’s maximum, and the null energy condition behind w ≥ −1 holds for any V (the bound itself also needs a positive energy density, which today’s dark energy has).
• The potential’s origin. Where τ’s potential comes from is open (Open: the origin of the ρ-preserving potential). The toy models show the structure is consistent, and #11 §10 adds: “None of this tests the cosmology”.

Superseded: DESI read as support#

Before round 3 the documents read DESI’s results as confirmation of the drift. The lab notebook called thawing “the sign pattern DESI reports” (#1 §7 item 2). The handoff called the sector “Consistent with DESI DR1/DR2 drift hints” (HANDOFF.md §2), DR1 being Data Release 1. v1 (#9 §8), the journey article #10 and the italic passage of #11 §10 describe DESI’s hints as exactly the drift the sector requires. The technical record of #11 §10 and the root CLAUDE.md replace those readings; what they left out is the phantom phase at higher redshift. The list is on DESI DR2’s phantom crossing.

Popsci-only: “constant is impossible”#

The destination article #12 states the requirement more strongly than the record: “Decreasing is required; phantom is impossible; constant is impossible”, and of the next data releases, “The framework survives only the first outcome” (‘Dark energy as the orientation of the split’). In #11’s row a constant −1 kills only the τ sector, and #10 agrees (“Constant kills the theory’s heart. Phantom kills it outright.”). The popular articles are never a source for a claim’s status (Conjectures: chat-only and popsci-only claims).

History of the row#

The row moved from 5 to 4 when the two clumping rows were withdrawn after Debt 3 (the history of the predictions table); the lab notebook’s v0.2 addendum lists it as “row 5 (thawing, no-phantom, DESI DR3)” among the program’s distinctive, still-live content. The only change of substance is v2.1’s clause on DR2.

Sources#

• CLAUDE.md ‘Since the handoff’ — “under real pressure ahead of DR3”
• papers/broken-born-checkpoint-v2.md §13 row 4 — the row; §10 — the field, its tags and the “Under pressure (v2.1)” paragraph; §15 — the exposure, “nearest trial” and the degeneration risk; header — the v2.1 change note; ref [21] — DESI DR2 Results II
• review/round3-adjudication.md ‘Rulings’ item 11 — the DR2 finding, accepted
• HANDOFF.md §2 — the external clock and the three outcomes; its “consistent” reading is superseded
• notes/broken-born-theory.md §7 items 1–2 — the no-phantom argument [D] and the thawing shape [T]; §3 — τ’s action; §9 — the v0.1 row 5; ‘Addendum (v0.2, post Debt-3)’ — the row among the live content
• notes/broken-born-program-v1.md §8, §9 — v1’s reading of DESI (superseded) and its row 4
• review/wiki-build-flags.md item 26 — DR3 as “three-year data”; item 27 — the potential’s sign, which bears on row 5 and on t_turn; item 6 — the vacuum-energy identity’s dependence on the flatness condition; item 43 — the corridor in the region of DR2’s fits, the slope that separates them, and the crossing redshift on which the pressure rests
• popsci/angle-of-the-mirror.md ‘The referee is already on the field’ and popsci/universes-other-half.md ‘Dark energy as the orientation of the split’ — “three doors” and the popsci-only “constant is impossible”; not status sources