Supernova Standard-Candle Hubble Diagram (2D)

Your model

Deceleration parameter q₀ -0.55

Hubble constant H₀ 67.7 km/s/Mpc

Fit to observed data (lower = better)

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Reference curves

Constant (q₀=0) Decelerating (q₀=+0.5) Accelerating (q₀=-0.55) Observed supernovae

Sample

Sample size 26

Observational scatter ±8%

Selected supernova

Redshift z

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Predicted (your model)

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Actual observed distance

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Apparent brightness vs. your model

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How it works

A Type Ia supernova always detonates with almost exactly the same true peak luminosity, so it works as a "standard candle": comparing its known true brightness to how dim it actually looks from Earth gives its luminosity distance directly. Independently, the stretch of its light's wavelength (redshift z) says how much the universe has expanded since the light was emitted.

d(z) ≈ (c/H₀) · [ z + (1−q₀)/2 · z² ]
q₀ = 0     → constant rate
q₀ = +0.5  → decelerating (gravity wins)
q₀ = −0.55 → accelerating (dark energy wins)

Drag q₀ yourself and watch the magenta curve — and the fit score — move. The real 1998 high-z surveys had to slide this dial until it landed near q₀ ≈ -0.55, discovering dark energy in the process.
H₀ rescales the whole distance axis (in Gly) without changing a curve's shape — it is a separate, independent unknown from q₀.
The plotted "observed" data always follows the accelerating curve with adjustable scatter, exactly like the real discovery data.
Click any yellow point to inspect that supernova's redshift, its distance under your current model, and its real plotted (observed) distance.

Constant rate Decelerating Accelerating Your model Observed SN Ia Selected

Click a point to inspect it · drag q₀ to fit