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In Type Ia supernova cosmology, the predicted apparent magnitude depends on the common absolute magnitude $M_0$ and the Hubble constant only through $\beta =M_0-5{\log }_{10}(H_0/H_{\mathrm{ref}})$, after choosing a fixed reference $H_{\mathrm{ref}}>0$. A flat improper prior on $M_0$ makes the likelihood integrated over $M_0$ independent of $H_0$, by translation of the integration variable. If the other prior factors are independent and the posterior is proper, the marginal posterior of $H_0$ equals its prior. An external calibration of $M_0$ can break this lack of identifiability.

A Type Ia supernova can be standardized as a standard candle by correcting its peak brightness using the light curve shape and colour index. Its host spectrum gives the redshift; the corrected apparent magnitude and calibrated absolute magnitude give the distance modulusThe resulting Hubble diagram measures the shape of the luminosity distance as a function of redshift. A spatially flat matter-and-vacuum model, for example, predictsNonzero cosmological spatial curvature changes both the expansion rate and the conversion from radial to transverse comoving distance. Comparing the observed Hubble diagram with these predictions constrains the matter density parameter, cosmological constant and cosmological spatial curvature; a single low-redshift observation cannot separate them. The nearby sample calibrates the common intercept, while distant Type Ia supernovae supply the redshift-dependent shape. Relative faintness at a specified redshift means a greater inferred luminosity distance.

Type Ia supernova cosmology requires correction for interstellar extinction, possible evolution of the standardized luminosity, and selection bias. The absolute magnitude–Hubble constant degeneracy means that an uncalibrated sample constrains the shape rather than independently determining $H_0$.

The flux relation is $F=L/(4\pi d_L^2)$ with luminosity distance $d_L=(1+z)\chi (z)$. In a spatially flat universe,Thus Type Ia supernova cosmology measures the distance-redshift curve. Equation (2) makes $H(z)$ depend on an integral of $w(z)$, while $d_L$ introduces a second integral. Fitting predicted distances to many supernova fluxes over a range of redshifts therefore constrains parameters or bins describing $w(z)$, although these integrations smooth fine redshift structure.

The common luminosity $L$ need not be known to constrain the shape of $w(z)$. An unknown $L$ multiplies every inferred distance by the same factor and is degenerate with the overall scale $H_0^{-1}$, or equivalently with the supernova absolute magnitude. Relative distances at different redshifts still determine the shape of the expansion history. An external calibration is needed to determine the absolute distance scale.

A standard candle is an astronomical source whose calibrated absolute magnitude or luminosity allows its apparent magnitude or flux to determine a distance. A population with unknown common absolute magnitude only determines relative distances without an external luminosity calibration. Type Ia supernova cosmology models this distinction explicitly.