Type Ia supernova cosmology

Type Ia supernova cosmology uses standardized supernova luminosities to measure the shape of the luminosity-distance--redshift relation. In a spatially flat universe,An unknown common absolute luminosity is degenerate with the overall distance scale but does not erase the redshift dependence.

A Hubble diagram plots a distance indicator, such as standardized supernova apparent magnitude or distance modulus, against redshift. The low-redshift relation sets a distance-scale intercept, while curvature of the relation at larger redshift tests the expansion history through luminosity distance. A common unknown absolute magnitude remains degenerate with the Hubble constant; the diagram's redshift-dependent shape can still constrain other cosmological parameters.

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.