= Type Ia supernova cosmology
{c}
Type Ia supernova cosmology uses standardized supernova luminosities to measure the shape of the luminosity-distance--redshift relation. In a spatially flat universe,
$$
d_L(z)=(1+z)c\int_0^z\frac{dz'}{H(z')}.
$$
An unknown common absolute luminosity is degenerate with the overall distance scale but does not erase the redshift dependence.
The useful observable is a relative <luminosity distance> at measured <redshift>, rather than an object's brightness alone. <Spectroscopy> supplies $z=\lambda_{\rm obs}/\lambda_{\rm rest}-1$; repeated <photometry> supplies a <light curve>. A <Type Ia supernova> is a <standardizable candle>: a fitted relation between <light curve> shape and <luminosity> replaces the incorrect assumption that every explosion has identical peak <absolute magnitude>. Nearby objects establish the relation and its common intercept; distant objects test its continuation and the shape of the <Hubble diagram>.
\Image[/supernova-standardizable-candle-readout.png]
{title=From repeated images and spectra to standardized brightness, relative luminosity distance and a conditional acceleration inference}
{description=Functional schematic with arbitrary illustrative light curves. The redshift and distance readouts are separate measurements; inference of acceleration requires a specified cosmological model.}
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