Compare cosmological models against Type Ia Supernovae data. Does the universe need a cosmological constant Λ, or does LFM explain accelerating expansion from first principles?
The 1998 Nobel Prize discovery: distant supernovae are fainter than expected in a matter-only universe, proving the expansion is accelerating. White dots = actual supernova observations.
Why do ΛCDM and LFM overlap? Because LFM predicts Ω_Λ ≈ 0.69 from χ field stability, which is almost identical to ΛCDM's fitted value of 0.685. The ~0.7% difference is smaller than observational error. This is LFM's success: it derives what ΛCDM must assume!
| Model | Mean Error | RMS Error | χ² | Free Params | Rank |
|---|---|---|---|---|---|
| LFM (Derived)BEST | 27.4% | 37.4% | 540.8 | 0 | #1 |
| ΛCDM | 27.5% | 37.4% | 541.0 | 2 | #2 |
| Empty Universe | 28.9% | 37.7% | 547.5 | 0 | #3 |
| Matter Only | 34.7% | 40.3% | 590.4 | 1 | #4 |
In 1998, observations of distant Type Ia supernovae revealed they were fainter than expected. This proved the universe's expansion is accelerating, not decelerating as expected from gravity.
Standard physics (ΛCDM) explains this by adding a cosmological constant Λ — an arbitrary parameter with no physical origin, representing ~68% of the universe's energy.
In LFM, dark energy emerges naturally from GOV-02:
The E₀² term represents vacuum energy required for χ stability. Setting E₀² = ρ_crit × c² gives:
ΛCDM fits Ω_Λ to match data (2 free parameters).
LFM predicts Ω_Λ ≈ 0.69 from first principles (0 free parameters).
Both match observations equally well, but LFM derives the answer rather than fitting it.
A universe with no matter or energy. Expands at constant rate forever. Clearly wrong for our universe.
The expected model before 1998. Contains only matter, no dark energy. Expansion decelerates forever.
Current concordance cosmology. Requires cosmological constant Λ as free parameter fit to SNe data.
Dark energy EMERGES from GOV-02 vacuum stability requirement. The E₀² term creates effective Λ without free parameter.