Euclid DR1 | Mode Identity Theory

Why Euclid Matters

In 2024, DESI (Dark Energy Spectroscopic Instrument) reported that "dark energy" may be changing over time. If true, it would overturn the cosmological constant (Λ) and reshape modern physics. Mode Identity Theory says the change is an illusion: Λ is fixed by the geometry of the universe, and what looks like evolution is the observer's phase position on a standing wave.

MIT predicts a specific shape (cosine, not linear), a specific zero-crossing (z = 0.663), and a specific constraint (Λ itself does not change). All values were deposited on Zenodo and MIT has no knobs to adjust. Euclid's independent measurement will either end MIT, ΛCDM, or both. Full stop.

Registration

All values were pre-registered on Zenodo in January 2026, months before DR1. The DESI DR2 analysis is a consistency check against already-public data. Euclid is the blind test.

Zenodo Pre-Registration

DOI10.5281/zenodo.18189079

RegisteredJanuary 2026

Phase offset δ−1.06 rad

Coupling ε0.255 (calibrated externally)

Free parameters for Euclid0

δ is fixed by registration. ε is calibrated from the DES-SN5YR + Planck + SDSS BAO combination (Abbott et al. 2024), which contains zero DESI data and zero Euclid data. Both values precede the data they are tested against.

Predictions

Modulation zero-crossing

The redshift where the surface-mode modulation cos θ(z) changes sign. Deterministic from δ via z_cross = 1 + δ/π.

MIT value

z_cross = 0.663

Falsified if

Non-parametric w(z) transition center < 0.4 or > 0.9 at 2σ

w(z) functional form

MIT predicts curvature: d²w/dz² ≠ 0. The cosine modulation is distinguishable from CPL's linear w₀ + w_a(1−a) template.

MIT value

Phase modulation (cosine)

Falsified if

Linear CPL preferred at ΔAIC > 4

Λ constancy

The cosmological constant is a surface-mode eigenvalue, fixed by boundary conditions. It does not evolve. What appears to evolve is the observer's phase position.

MIT value

Constant

Falsified if

Binned ρ_DE(z)/ρ_DE(0) departs from unity at 2σ

No phantom crossing

MIT's exact w_eff(z) > −1 at all redshifts. The apparent crossing reported by DESI is a CPL template artifact, arising because the linear form absorbs the cosine shape.

MIT value

w_eff > −1 everywhere

Falsified if

Model-independent reconstruction confirms w < −1 at 2σ

The mechanism

MIT holds Λ fixed by topology. The cosmic standing wave Ψ = cos(t/2) modulates the dark energy surface mode, leaving matter and radiation untouched. When observers fit distance data using fluid-based models, the phase structure leaks into apparent w(z) evolution.

MIT Friedmann equation

E²(z) = Ω_m(1+z)³ + Ω_r(1+z)⁴ + Ω_Λ^bare[1 + ε cos θ(z)]

Phase-redshift mapping

θ(z) = (2π + δ) / 2(1+z)

The modulation is invisible to the CMB by construction: Ω_Λ^bare/E²(z_*) ~ 10⁻⁹ at recombination. It becomes observable only at low redshift, where Ω_Λ dominates the energy budget. The deviation from ΛCDM peaks at ~4.6% near z_cross = 0.66, falling to zero at z = 0 (normalization) and z ≫ 1 (matter dominance).

Why this is testable

CPL uses two free parameters (w₀, w_a) to fit the shape. MIT uses zero free parameters for the shape: δ is fixed, ε is calibrated externally, and the cosine form follows from the axioms. A purely linear w(z) at high precision would falsify the phase modulation signature.

DESI DR2 consistency check

The DESI analysis uses already-public data. It is a consistency check, confirming the modulation template is compatible with current BAO measurements. It is not the blind test.

Model	Parameters	χ²_BAO	χ²_total	ΔAIC vs ΛCDM
ΛCDM	2	13.54	1419.58	0
MIT (ε = 0.255)	2	11.21	1417.45	−2.1
CPL	4	8.58	1411.55	−4.0

Combined analysis: DESI DR2 BAO (13 observables, 7 bins) + Pantheon+ (~1590 SNe) + Planck-calibrated H₀r_d prior. MIT improves on ΛCDM at the same parameter count. Profiling ε yields Δχ² = −7.9 at ε = 0.16 (ΔAIC = −5.9 at k = 3).

Timeline

July 2023

Euclid launch

SpaceX Falcon 9 from Cape Canaveral. Transit to L2.

November 2023

Early Release Observations

First processed images. Showcase of wide FOV, resolution, low-surface-brightness detection.

February 2024

Science survey begins

Routine observations start. ~100 GB/day.

March 2025

Quick Data Release Q1

Three deep fields, 63 sq deg, 500+ strong lenses. No cosmology.

January 2026

MIT values deposited

δ = −1.06 rad, z_cross = 0.663 sealed on Zenodo (DOI).

June 2026

Q2 release

Second quick release. Pre-DR1 data products.

21 October 2026

DR1: First cosmology data

~2,300 sq deg. Weak lensing, galaxy clustering, BAO, photometric redshifts. First cosmology release.

What Euclid DR1 delivers

DR1 contains the first year of survey data: ~2,300 square degrees of sky, plus accumulated deep field passes. This is the first Euclid release with cosmology results.

DR1 product	MIT relevance	What to watch
Weak lensing (cosmic shear)	Constrains Ω_m, w₀ independently of BAO	Does the shear power spectrum prefer w₀ > −1?
Galaxy clustering (spectroscopic z)	BAO standard ruler, independent of DESI	New BAO measurements across Euclid's redshift bins
Photometric redshifts	Galaxy distribution, tomographic bins	Precision at z ~ 0.5–0.8 (near z_cross)
Strong lensing (~7,000 candidates)	Geometry probe via D_d/D_s ratios	Independent distance ratios through the z_cross window
Higher-order WL statistics	2.5× more sensitive to w₀ than 2-point	Sensitive to the shape of w(z), not just the value
Galaxy cluster abundance	σ₈, structure growth rate	Growth vs. expansion history consistency

Key advantage

Euclid's weak lensing and galaxy clustering are complementary to DESI's BAO. They constrain the same underlying physics through different observables and different systematics. Separate instrument, separate team, separate data.

Papers

Paper	Reference	Status
Λ Constant, w Evolving	Zenodo	Registered
Mode Identity Theory (Engine)	Zenodo	Registered
Λ Ground Mode of the Cosmic Boundary	Zenodo	Registered
Λ Constant, a₀ Evolving	Zenodo	Registered
Euclid DR1 results	TBD	Awaiting