Dark Energy and the Crust

DESI DR2 as Evidence for Cyclic Boundary Encounters

The DESI anomaly

The Dark Energy Spectroscopic Instrument’s second data release (DESI DR2) found that the dark energy equation of state is not constant.¹ In the standard CPL parameterization w(z) = w_0 + w_a \cdot z/(1+z), the best fit lies far from the cosmological constant (w_0 = -1, w_a = 0), with ΛCDM excluded at more than 2\sigma. The data prefers dark energy that was phantom (w < -1) in the recent past, crossed w = -1 near z \approx 0.5, and was quintessence-like (w > -1) before that.

This is a problem for ΛCDM. A cosmological constant does not evolve. But it is also awkward for most dynamical dark energy models, which predict smooth monotonic evolution — not the non-monotonic shape that the DESI data imply. The equation of state appears to have structure: a feature near z \approx 0.5 and a deep phantom regime at z > 1 that a simple scalar field cannot produce without significant fine-tuning.

What the substrate predicts

The substrate framework provides two independent mechanisms that together produce exactly the shape DESI observes, with distinct physical origins.

Mechanism 1: The bulk deficit (Volovik self-tuning)

From Gravity §G4–G5: in thermodynamic equilibrium, the substrate’s vacuum energy is exactly zero. The Gibbs-Duhem relation at T = 0 gives \varepsilon + P = 0 with \varepsilon = 0 — the superfluid self-tunes. The observed dark energy is entirely a residual from cosmic expansion preventing full relaxation:

\rho_\Lambda = \rho_\text{substrate} \cdot (\delta T / T_c)^2

This means dark energy was less in the deep past, when the universe was closer to equilibrium. The disequilibrium builds up during the matter-dominated era as the expansion rate evolves. At high redshift, dark energy approaches zero — not a constant.

This produces a deficit in the dark energy density relative to today’s value: the further back in time, the less dark energy there was. In the equation of state, a decreasing f(z) at high z drives w below -1 — into the phantom regime — because the energy density is falling faster than a^{-3(1+w)} with w = -1 would predict. The phantom crossing is not exotic physics; it is the signature of a dark energy density that was simply smaller in the past.

Mechanism 2: The crust (boundary encounter)

From A Universe That Boils: our observable universe is a bubble that nucleated inside a metastable substrate. The bubble wall expanded through the surrounding medium. That medium was not empty — it was the remnant of a previous cycle’s relaxation, containing organized energy in its boundary structures.

When the bubble wall passed through this crust — the remnant boundary layer of the previous cycle — it absorbed energy. That energy was deposited into the dark energy density of our universe at the redshift corresponding to the encounter. The crust acts as a bump in the dark energy density, localized near a characteristic redshift z_s set by the geometry of the previous cycle’s remnant.

The crust energy rises as the bubble wall enters the boundary region (z > z_s), peaks near z_s, and decays exponentially as the wall moves past it. This produces a localized enhancement — more dark energy near z_s than the bulk evolution alone would give.

The combined model

The two mechanisms combine into a single density profile:

f(z) = 1 + B \cdot z \cdot e^{-z/z_s} - C \cdot \frac{z^2}{z^2 + z_b^2}

where f(z) \equiv \rho_\Lambda(z) / \rho_\Lambda(0) is the dark energy density normalized to today’s value, and the equation of state follows from:

w(z) = -1 + \frac{(1+z) \cdot f'(z)}{3\,f(z)}

The first term (crust) is a bump that peaks at z = z_s with amplitude \sim B \cdot z_s / e. The second term (bulk deficit) is a smooth suppression that saturates at -C for z \gg z_b, with onset near z_b.

Parameter status

The model has four parameters. Their physical status within the framework is sharply different:

Parameter	Value	Status	Physical meaning
C	1.0	Predicted	All dark energy is transient (Volovik: equilibrium DE = 0)
z_b	2.20	Derivable	Matter→Λ transition onset (from \tau_\text{relax}, C7, S4)
B	1.88	Fit to data	Crust energy density (previous cycle property)
z_s	0.63	Fit to data	Crust location (previous cycle geometry)

C = 1.0 is the Volovik prediction. This is the most physically significant result. In the high-redshift limit:

f(z \to \infty) = 1 - C

Setting C = 1 gives f \to 0 — dark energy was zero in the deep past. This is exactly what the substrate framework predicts from first principles. G4 states it explicitly: the Gibbs-Duhem relation at T = 0 drives the vacuum energy to zero at equilibrium. G5 says the observed \Lambda is entirely a residual from disequilibrium. The fact that the best fit to DESI data lands on C = 1.0 means the data is saying: all of today’s dark energy is transient. There was none in the deep past. The substrate was at equilibrium, and the subsequent disequilibrium plus crust encounter built up everything we now observe.

If C had come back as 0.3 or 1.7, the model would have a fit but not a prediction. C = 1.0 is the specific value the framework predicts independently of DESI.

z_b = 2.20 should be derivable. The onset scale of the bulk deficit tracks how fast the substrate’s disequilibrium builds during the matter→Λ transition. From the relaxation ODE:

\frac{d(\delta T)}{dt} = -\frac{\delta T}{\tau_\text{relax}} + \alpha \cdot H(t)

the scale z_b should satisfy H(z_b) \cdot \tau_\text{relax} \sim 1 — the redshift where the relaxation timescale matches the Hubble time. If \tau_\text{relax} can be derived from C7 and the substrate parameters (see Constraint Summary), z_b becomes a prediction.

B and z_s are genuinely free — they describe properties of the previous cycle’s remnant, which are inherently cycle-dependent and not predictable from within a single cycle. This is not a deficiency; it is the correct parameter count for a cyclic model. The crust amplitude (B = 1.88) says the bubble wall absorbed about 44% excess energy density at peak. The crust redshift (z_s = 0.63) corresponds to a lookback time of about 5.6 billion years — when the bubble wall was passing through the densest part of the old boundary.

The fit

With these four parameters — two predicted or derivable, two fit — the model reproduces the DESI DR2 constraints within 1\sigma in the w_0–w_a plane. The w(z) curve tracks the DESI best-fit CPL shape across the full redshift range 0 < z < 3. The combined curve in the density panel is virtually indistinguishable from the DESI-implied profile — the dashed DESI reference line is barely visible behind the model curve.

The model naturally produces all the qualitative features the data requires: phantom behavior (w < -1) at z > 1 from the bulk deficit; a phantom crossing near z \approx 0.5 from the interplay of crust and deficit; and the return toward w = -1 at low redshift as the crust contribution fades.

What makes this different

The CPL parameterization w(z) = w_0 + w_a z/(1+z) is a phenomenological fit with no physical content. It has two free parameters and captures the gross features of the DESI data, but it does not explain why dark energy evolves, what produces the phantom crossing, or what sets the scales.

The substrate crust model has four parameters, but two of them are either predicted (C = 1.0) or derivable (z_b from relaxation dynamics). The remaining two (B, z_s) describe the crust — a specific physical object (the previous cycle’s remnant) that the framework already requires for independent reasons (see A Universe That Boils). The crust was not invented to fit DESI. It was already part of the cyclic cosmology picture. The DESI data simply provide the first observational evidence for its existence.

The key discriminators:

1. C = 1 is a zero-parameter prediction. The Volovik self-tuning mechanism requires dark energy to vanish at equilibrium. The best fit confirms this.

2. The phantom crossing has a physical mechanism. It is not a parametric accident — it is the transition between crust-dominated (quintessence-like) and deficit-dominated (phantom-like) regimes. The two components have different physical origins and different redshift dependences.

3. The model predicts specific shapes, not just (w_0, w_a). The density profile f(z) has a distinctive bump + deficit morphology that is sharper and more structured than any monotonic quintessence model. Future surveys (DESI DR3, Euclid, Roman) will resolve this shape and provide a clean test.

4. The crust provides evidence for cyclic cosmology. If confirmed, the bump at z \approx 0.63 is a direct detection of the previous cycle’s remnant — the first observational evidence that our universe nucleated inside a pre-existing medium.

Toward a 2-parameter model

If z_b can be derived from the relaxation ODE — connecting \tau_\text{relax} to H(z) via the Friedmann equations and the substrate parameters from C7 — the model reduces to:

• Zero-parameter background: C = 1 (Volovik), z_b from relaxation dynamics
• Two-parameter crust: B and z_s (previous cycle properties)

This would be a model where the only free parameters describe the crust, which is inherently cycle-dependent and not predictable from within a single cycle. Everything else — the entire background evolution of dark energy — is determined by the substrate physics already established in the constraint system.

The derivation requires solving:

\tau_\text{relax}(z_b) \sim 1/H(z_b)

with \tau_\text{relax} computed from the substrate’s viscous response (C7, the Volovik relaxation mechanism) and H(z) from the Friedmann equations with \Omega_m = 0.315. The condition H(z_b) \cdot \tau_\text{relax} = 1 determines z_b as a function of known substrate parameters. This is a well-posed calculation.

Connection to the constraint system

The DESI result connects to three existing elements of the constraint system:

C7 (cosmological constant): The bulk deficit term directly implements the Volovik self-tuning from G4–G5. The disequilibrium fraction \delta T/T_c \sim 10^{-61.5} describes today’s residual; the z-evolution of this residual through the matter era is what z_b captures. The DESI fit provides the first empirical constraint on the time evolution of the disequilibrium, not just its present-day value.

S4 (Friedmann equations): The Hubble rate H(z) enters both the DESI comparison (through the distance-redshift relation that converts BAO measurements into w(z)) and the relaxation ODE (through the driving term \alpha \cdot H(t)). Self-consistency requires that the same H(z) that fits the BAO data also drives the substrate relaxation that produces the deficit.

The cyclic cosmology (A Universe That Boils): The crust term is the first quantitative evidence for the boiling-universe picture. The existence of a localized energy feature at z \approx 0.63 — not a smooth background, but a bump with a specific redshift and amplitude — is what you expect if the bubble wall encountered a boundary layer. The crust parameters (B, z_s) become the first empirical constraints on the geometry of the previous cycle.

DESI reference data

The fit uses the DESI DR2 + CMB combined constraints:²

Quantity	Value
w_0	-0.42 \pm 0.21
w_a	-1.75 \pm 0.58
Correlation \rho_{w_0, w_a}	-0.85
\Omega_m	0.315

The error ellipse in the w_0–w_a plane is rotated by \sim 17° from the w_0 axis, with semi-axes (0.160, 0.920) and (0.262, 1.508) for the 1\sigma and 2\sigma contours respectively.

Open calculations

1. Derive z_b from \tau_\text{relax}. The most important next step. Compute \tau_\text{relax} from C7 and the substrate viscous parameters, then solve H(z_b) \cdot \tau_\text{relax} = 1 for z_b. If z_b \approx 2.2 falls out, the background is fully determined with zero free parameters.

2. Compute the crust energy budget. The amplitude B = 1.88 implies a specific energy density absorbed from the previous cycle’s remnant. This should be consistent with the nucleation barrier energy from the dc1/dag free energy landscape (open problem 1 in Universe That Boils).

3. Predict f(z) shape for future surveys. The density profile f(z) has distinctive curvature (concave near the crust peak, convex in the deficit region) that differs from CPL or any polynomial dark energy model. Euclid and Roman will measure w(z) at higher resolution — the model predicts specific deviations from CPL that are testable.

4. Check consistency with CMB. The high-redshift behavior f(z) \to 0 for C = 1 affects the integrated Sachs-Wolfe effect and the late-time ISW signal. Verify that C = 1 is consistent with Planck CMB constraints independently of the BAO data.

5. Connect to a_0(z) evolution. The MOND scale a_0(z) = a_0(0)(1+z)^{3/2} from Galactic Dynamics is affected by the crust — the crust modifies the local dark energy density, which feeds back into the substrate disequilibrium. At z \sim z_s, there may be a detectable modulation of the MOND scale. This is a cross-domain prediction connecting galactic dynamics to cosmology through the crust.

Footnotes

1. DESI Collaboration, “DESI 2024 VI: Cosmological Constraints from Baryon Acoustic Oscillations,” arXiv:2404.03002, 2024. Updated in DR2, 2025. The CPL parameterization gives w_0 = -0.42 \pm 0.21, w_a = -1.75 \pm 0.58, with the cosmological constant (w_0 = -1, w_a = 0) excluded at > 2\sigma.

2. DESI Collaboration (2025), DR2 combined analysis.